You didn't say if you're running the stock game or a mod - To tell you the truth I can't remember much about the stock game now
, but I think you can access the large area chart from it - it's attached to the shortwave radio, which you can get to either via the radio room or the menu bar.
Anyway, the map has the traffic lanes on it. find the ones that cross your patrol area and plot a course that cuts them. either zigzag along them or plot a box pattern that give you a lane about 10 miles wide. If there are no obvious traffic lanes then plot lines between nearby ports, the bigger the better, then plot a search pattern along those lines in a similar way. The vanilla game gives you lots of sighting reports. Supermods less so. When you get one within a couple of hundred miles, plot its course, note its speed and stick a compass circle on it and update it every hour with the distance travelled. before I started using mobo to plot intercepts I'd just make for the course track at my best speed and then zigzag down it until I made contact.
The game will lag when it's generating a contact and it's very noticeable in time compression. I think of it not so much as a cheat, as my crew paying attention all of the time and alerting me when they spot something. Anyway, when the game suddenly seems to stutter, drop out of time compression and check your sonar. Chances are that if you haven't been informed of a contact, and there's one close, that's where it will show up. Your sonar operator won't report a contact until it gets within the effective range of the gear that's currently installed, but using it manually, you can hear contacts much further away. There are lots of resources on here for plotting course and speed using only sonar. If you have radar, then you can just head towards the sound at best speed until you pick him up that way. likewise, you can just do the same thing until you pick him up visually and take it from there.
Anyway you should get some results from one of these methods. they're all quick and dirty, and capable of much refinement. Learning that, is lots of fun too. Good hunting