Jayni,
Generally once you get a target you want to move toward it. see if you can figure out or see which way its headed. Once you know, adjust your course to intercept it, so go to where it is headed instead of where it is. As you close you may get additional contacts and the tactical situation will become more clear.
Sometimes you are lucky and its headed right for you or in your general direction. Sometimes its headed away from you - so you have to decide if you want to burn the fuel to chase it or just let it go (assuming you aren't using the Nuke Boats Mod LOL). If you do chase, remember to go AROUND it as you close, so that you don't run up on the tail of a convoy and get forced down by escorts. The ole "end around" run is still the best way to do things, though it takes patience.
I can't speak for others, but I never run a "search pattern" once I get to my patrol area. In my mind, its just burning fuel (or battery) that you might need for later. Hydrophones - and radar when you have it are more than sufficient to find targets most of the time.
Good Hunting!
For future SH4 gameplay questions, the sub-forum below is where you will want to go.
http://subsim.com/radioroom/forumdisplay.php?f=202