Red October1984, you must read the manual.
Everything you need to know is in the manual. It even gives some suggestions on tactics to use.
Use acoustic conditions to your advantage. The most basic thing here is the thermal layer, which you (or enemies) can hide under (or above). There is also "noisy" water sometimes (generally in deep water). Use the Shift+F8 key to display these conditions.
Pay attention to your sensors. The towed array is the best sensor you have, but it won't always work. It is only operational in deep water, and when your sub is moving steadily. Quick turns will temporarily disable the towed array.
Be mindful of the enemies detection abilities. Compare sonar with enemy contacts using the F7 key.
Keep a copy of the keyboard layout on hand. When things start moving quickly you might get flustered. Pause the game until you find the keys you want to press.
Keep quiet. A submarine's best advantage is its stealth. Avoid fast speeds, using the periscope and active sensors.
Once you've made contact with the enemy you cannot return to transit (strategic) mode until you have dealt with the enemy. You can destroy them or sneak away. Once you have no more contacts, or your contacts are moving away quickly, you will have the option to end the battle and return to transit.