Otto Kretschmer[en.wikipedia.org] is widely regarded as (one of) the most successful uboat commanders of World War 2.
Across 16 patrols, he was responsible for sinking 46 ships for a total of 273.043 GRT, more than any other uboat ace.
During his command of U-99, he became famous for his night-time attacks and his motto "One torpedo, one ship". On the 16th of March, 1941, his boat was hit by depth charges and driven below the technical crush depth before resurfacing and scutting the boat. He and his crew, except for three men who lost their lives, were taken as prisoners and survived the war.
After the war, he rejoined the Deutsche Marine with the rank of Commodore. He died in 1998, his ashes scattered at sea.

As well as the astonishing results achieved by the boats under his command, he is remembered for his 11 points of Submarine Warfare, which partially contradicted the contemporary German doctrine.
I present to you these 11 points, along with some observations related to their implementation in-game, to inspire and guide you during your gameplay. Please let me know of any inaccuracies or syntactical errors I might have committed, and feel free to contribute.

Manually use the UZO to have a better chance of detecting traces of enemy activity

Your Uboat has a pair of ears and a pair of eyes. The latter is made up of your watchmen: having a Leader officer at all times on watch duty is of prime importance to spot far away convoys via their smoke trails and, most importantly, incoming warplanes. During an air attack, a few seconds can be the difference between getting hit and being able to submerge with impunity.

Organize your Leaders in shifts, to ensure watch duty is being provided for at all times, and aim to get a third Leader officer to delegate lesser jobs to, such as navigational accuracy/cooking/playing cards. If there's any station that should be getting the 2 additional sailors you can assign to an officer, it's probably the Observation Deck.

In the Maschinenraum, your machinists will work relentlessly to intercept your target

While it sounds more like life advice than an in-game tip, spotting a convoy at the right time can be the difference between a successful attack and a failed one (with all the consequences failure might imply). Timely spotting a convoy is vital in:

• successfully organizing an interception
  
• obtaining an optimal attack position
  
• securing escape routes after the attack is carried out

Each one of these points hides additional significant value: e.g., successfully organizing an interception doesn't mean merely managing to reach the objective, but managing to do so at the right time and place. Failing to timely spot the convoy might cause you to spend more fuel, to finally catch up with it during daytime and ending up too close to the well-protected British mainland, making it impossible to wait for the cover of the night to carry out an attack.

Moreover, obtaining an advantageous position means you can carry out the attack completely on your terms, preventing you from having to rush things and make questionable decisions to complete your objective before dawn. It also can mean you can take your time when you slip out of the convoy.

HE shells are more likely to cause fires

This one should be pretty obvious, but for those to whom it's not, let's explain it.
Torpedoes are your most powerful weapon: they carry a considerable explosive payload, and by nature, they strike below the waterline, where a ship is most vulnerable. A single torpedo hit is usually enough to sink all but the most resilient freighters, and it's pretty much a guaranteed kill on a loaded tanker. They're slow and require accurate targeting and positioning to employ, though, and most of all, they're not expendable. Having to be at sea with no torpedoes most often means wasting time.
Torpedoes also are the only weapon you can use while submerged, thus effectively being your only way to send a ship down whenever there is a warship around (they also are the only weapon you can hope to effectively use against warships themselves!)

Your deck gun, and, to an extent, your flak gun, are secondary weapons you can only use while on the surface and are much less powerful than torpedoes. However, you can carry much more ammunition for those, meaning that missing a shot has less dire consequences. Using your surface guns against unescorted/unarmed targets means saving valuable torpedoes for another encounter.
Remember to aim at the waterline, and don't underestimate your HE flak gun ammunition's capability to damage surface ships.
Do not attempt to use your secondaries against warships, however: they're much better equipped for surface warfare and you won't stand a chance.

You can interact with the sailors of sunken ships

Not all that is good is lost in war: more often than not, when given the chance, uboats would help the survivors of the ship they sank.
Since we're only sinking virtual ships manned by virtual sailors, there is no real moral value in helping any survivors. However, keep in mind that rescuing and once at port releasing sailors provides you with an increase in reputation. All lives are equal, but the lives of captains and engineers are more equal than others, and will grant more reputation points.

Attacking a convoy during daylight will require you to attack submerged, which poses additional challenges

When we talked about the timely spotting of targets, we mentioned being forced to attack during daylight as a possible consequence of failing to implement it.
If it is your last chance to attack a convoy before it reaches the air coverage of the RAF, you might be forced to attack during the day. This means you will most likely have to do so submerged, which means that

• you won't have any real speed advantage over the freighters, making repositioning extremely hard to do and virtually impossible without giving away your position or disengaging and reengaging
  
• you won't be able to quickly disengage, because your speed will be limited both by water resistance and the noise you'll be emitting
  
• the escorts' hydrophone/SONAR will be able to detect you, and this is particularly bad news because they will be able to depth charge you, and because you're more audible underwater than visible on the surface during nighttime

A nighttime torpedo hit will suddenly light up the otherwise dark convoy

I'm not entirely certain about the degree of simulation the game offers, but it is to be noted that realistic systems for visual detection are in place. Among those (most of them, you can view by hovering with your mouse over the detection hint in the lower right part of your screen) is time of day and visibility. At night you'll be less visible, but the moon might make it harder or easier for you to be spotted.
Since I'm not sure if the uboat silhouetting in the moon reflection is a thing in game, I'd advise you to attack from the direction that gives you the best view of the enemy, be it from the dark side or the bright one.

Crew resting in the bugraum

Here the suggestion is to let the wind help you quietly slide on the surface when moonlight is not an important factor.
Since there is no such simulation in the game I know of, we'll use this section to give off some miscellaneous tips:

• the way your boat is oriented influences how easily spottable it is: the uboat is much harder to see when it's facing the observer and has a bigger shape when viewed from the side. Keep this in mind when maneuvering around convoys.
  
• the same applies underwater: a front-facing uboat has a significantly smaller ASDIC signature than one pinged by the side
  
• ASDIC has a blind spot below the keel of the ship. When a destroyer is depth charging you, they have already lost contact and are dropping the bombs where its crew predicted you'd be. You can use this moment to suddenly change speed, course, and depth to avoid the charges and slip away. The introduction of the hedgehog, however, will let the enemy attack you while keeping you in sight.
  
• both ASDIC and hydrophones have a blind zone behind the ship. The noise of their own propellers makes detecting foreign noise impossible. This is also true for your own ship.
  
• when taking in water while submerged, you can trim your ballast by right-clicking on the valves with an officer. This expels enough water from the ballasts to keep the boat's buoyancy neutral, accounting for the water in the internal compartments. If you feel you're not going to make it, emergency blow the ballast to use all your compressed air to blow the tanks to buy you time.
  
• the deeper you go, the less effective your pump becomes, due to the external pressure
  
• your diesels leave a smoke trail that can be spotted by the enemy. You can reduce it by lowering your speed or by having a Chief Engineer officer with the proper skill to manage the engines.
  
• laying on the seabed, where possible, will greatly reduce your ASDIC signature, as you will blend in with the seafloor. The enemy can still hear you over the hydrophone though, so make sure to be very quiet, as you'll be more vulnerable.
  
• you can heat your torpedoes before engaging the enemy in order to reduce the risk of a missed or premature detonation
  
• by using the three buttons every compartment has available in it's bottom left corner when in third person mode, you can cut electricity to a compartment, evacuate it or order to carry the water to the main room (where the bilge pump is most effective)
  
• keep in mind that if you close the bulkhead of a flooding compartment, opening it might become difficult due to the pressure the water excercises on the other side
  
• you can approach and inspect vessels flying neutral flags to make sure they're not smugglers helping the enemy

Most of the time, a single torpedo will be more than enough to do the job

Torpedoes are powerful weapons, the deadliest in fact, at least until the introduction of the naval missile. They're slow and, for most of the war, dumb, and sometimes even unreliable, but a torpedo hit will have devastating consequences on the capabilities of a ship of staying afloat.
Since they're limited in numbers, reasoned use is necessary if one wishes to be most effective.
Their warhead will often be more than enough to set big fires alight, cause secondary explosions, and to outright prompt the evacuation of the ship. Keep in mind that some of the torpedoes you carry on board, especially during the first years of the war, might have defective pistols, preventing them from detonating on the target and thus effectively reducing the actual amount of killshots you have available. Only big warships and the most resilient and lucky freighters will require more than one torpedo to be sunk.
If your objection to this point is "double the bullets, double the accuracy", keep on reading to the next point.

Half the distance, double the accuracy

Torpedoes can be nasty. Some are slow, requiring careful aiming, some don't work and all they'll cause their target is an ugly dent on the hull. Wasting one is something you should avoid, and the best way to not waste a good torpedo is to have a good fire solution.
A fire solution is a series of parameters that ultimately determine the course the torpedo will follow and its point of impact. You will have to determine your fire solution by measuring the target's speed, course and distance. The more accurate those measurements, the more accurate will the fire solution be.
However, these measurements often take time, and sometimes are inaccurate no matter what due to fog, bad visibility, heterogeneous movement of vessel and target and strong winds.
Taking a closer shot has the following advantages:

• you don't need to be as accurate (even course errors of tens of degrees won't matter)
  
• since you don't need to be as accurate, you use less time per shot and can thus take more shots at more targets
  
• being closer will make the measurements much easier

This, of course, comes with the disadvantage that it will be much harder to set up an attack without being detected. It'll be up to you to determine if this is the course of action better suited to your style. And do keep in mind that torpedoes have a minimum arming distance, so firing point blank will result in hearing a "thud" instead of a "boom".

This Uboot has been spotted by a plane while conducting a search of a ship flying a neutral flag. To ensure its survival, it must scramble to dive

The Uboat is a nimble vessel. It's low on the water, only the conning tower being significantly visible, it has a very low side profile and an even slimmer front profile. It is really hard to spot even during the daytime, and even more so during darkness. If you manage to stay undetected until the moment the torpedoes go off, even when alerted by the explosions the enemy watchmen will still have to spot you. By taking advantage of the valuable seconds between the moment you empty your tubes and the moment they start looking for you, you can move further away and make your detection even harder. You can extend this time by firing slow torpedoes. Remember that the soldiers on navy ships are much more trained and capable of spotting you than sailors aboard merchants.
If you get spotted and have to crash dive, it means you lost your initiative. The ball will now be in the escorts' court: they'll start to track you via hydrophone and even try to pinpoint your exact position by using the more advanced ASDIC. You'll now have to endure relentless attacks by depth charges, hoping to survive to the moment they run out of wasserbomben or you get an opportunity to slip away, aided by the bombs' echo.

However, we know that eventually the Allies will develop ways of detecting you without having to see you even on the surface, namely the radar, making surface attacks an obsolete tactic.

Your hydrophone operator can detect convoys from afar

Your hydrophone is your best chance to detect far-away convoys: bigger groups can be heard dozens of kilometers away. You should regularly conduct hydrophone checks to maintain awareness by submerging and silent running your boat. Your technician officer will then be able to pick up noise made by propellers of enemy formations.

It should be noted that with the war going on you will not be able to maintain this point, due to Allied technological innovation that makes the surface dangerous for a uboat, forcing you to only surface at night and to use snorkel during the day.

Keep in mind some of these points can only be effectively applied up until a certain point in the war. Radar will make surface activity ever more dangerous. Some points do not necessarily make sense in-game either.
You don't have to follow these points, as many other skippers did not. These are Otto Kretschmer's principles, which he successfully applied, and are not necessarily a tutorial. The best way to play is the one you feel most comfortable with, the one that lets you achieve the best results, and, ultimately, the one you enjoy the most and have the most fun playing.

I'll update this guide with a few more tips and tricks and a mod collection I recommend you play with to have a more immersive experience.
Any feedback is greatly appreciated.

Thank you for reading up to this point.