First, avoid passing in front of escorts. Try to pass on their side or
behind them. On the map, draw circles with your maximum torpedo range and try to shoot as far as possible, within this range (5 km for type II torpedoes, 5/7.5/12.5 according to speed level for type I). Since the type I torpedoes leave a bubble trail, get closer.
Don't let periscope up too long. No more than one minute at any time, within 30 seconds if you can. Try to keep the periscope as close to water level as possible, move it up/down as required all the time.
Always check depth under keel before attaking. It uses active sonar to do so, and if you ever check depth with an escort around or after having being detected, you will make so much noise they will now exactly where you are. You spot a ship ? Check depth. If it's small, attack from as far as possible, and turn around, dive, and stop engines and wait for explosions.
If you can, attack at night. If you spot a ship or convoy during day and its speed is not too fast (ex. slow) you can plot their course, and "Shadow" them. Running 10 Km or so away on parralel course until it's night. At night the wakes from the type I torpedoes won't be seen at all or easily, and your periscope won't be spotted as in day. Attack when sun is going down but not totally dark since most ships run all lights turned off, if it's a night without moon you will have trouble seeing the ships.
Attack from the side, at 90 degrees. I prefer to attack when I have ships on my left going right. I always try to shadow and attack when sun goes down or at night (with my current type IIA it's sometimes impossible because I don't have enough speed to keep with most convoys).
If you are detected, it's easy. Escorts start pinging (which means you passed in front of them), lights on surface search for you or bullets start to get fired at your periscope
Dive. Not too deep. enough to have margin to evade depth charges. Do not dive to maixmum depth yet. Dive, and type about 10 meters between you and ocean floor if it's not too deep.
Intead of letting your hydrophone operator report to you, get to his place and go a 360 degree check with engines turned off. Check where the nearest warship is. Listen to it without moving the needle and the sound is going to fade : check if it goes left or right so you know where it is and where it is going. Get to map, use the ruler to plot it's line of bearing. Start engines, use slow speed and move away from this line at 90 degrees. Always try to show the smallest profile to your enemy : front or back. never your side because that makes you a big juicy target for ASDIC (the real name for the sonar they use).
If it gets close, order silent running. Click on the speed thingie, and click to set speed between 0 and 1. The guy will report "Setting speed to 0 knots" but in reality, you are not setting speed to 0 but to 1. In the sub, above the two guys that steer the sub, you can see the two engine RPM values. If you order slow speed while running silent, it's still 150 or 200 RPM or so. When you order a speed with the needle at 0/1 it will go t0 50 RPM. That's the best : 50 RPM will give you 1 knot but it's damn silent, more than the default "Run silent running!" setting.
Watch out : using slow speed makes the sub difficult to keep at ordered depth and you will go 5 meters or so higher. Order a deeper depth, about 5/6 meters deeper than you want (the ballasts are not used for dive control but neutral buyancy, the engines and the diving planes are used to level the sub at the desired depth, even modern subs do it like that. It's only when speed is 0 than ballasts are used to go up/down but they do noise so avoid going up/down with engines stopped).
If the escorts is pinging you, no need to remain silent. They know where you are, you are directly under them. Remove silent running, move to standard ahead. Find where the escort is, and where it is going (either ask the hydrophone operator to track it, and rapidly check on hydrophones). When it gets closer, order flank ahead speed and move the sub 40 degrees left or right and get out of the place they're gonna throw depth charges as fast as possible. While charges are exploding they are not hearing : as soon they start exploding, change course again and full speed. Always dive when doing so : that's why you keep 10 or 20 meters below you, so you can go flank ahead, change course AND dive at the same time for at least 10 meters deeper than where they detected you to avoid their depth charges).
As soon the depth charges stop exploding, order silent running. Set speed to 50 RPM, change course again and go up 10 meters or so or keep current depth (always make sure you can dive for 10 meters anytime. Go deeper and deeper, and if you're too close to ocean floor or near crush depth, go up 20/30 meters).
Do not always run flank ahead speed even if they're pinging. Sometimes they are pinging but you are not under the pings. Be clever. Unless the operator says they are pinging you, keep silent. Find where they are, show them the smallest profile (make them see your front of back of sub, never the side).
Also, if you have a merchant ship stopped after a torpedo attack, try to get below it. The escort cannot go over a ship on surface, so it is a very good spot to hide because they escorts won't easily pass over you. If the merchant goes down.. Get the hell out of there (so don't park just below it...).