The following video tutorial explains how to use the radar station and the navigation map during the approach phase, that is from the moment the target is detected in the radar up to the moment your submarine is positioned and ready to enter the attack phase.
Basically, the process consists of estimating the distance and course of the target and moving your submarine, based on that information, to a position of advantage for the attack; all that without being detected of course.
The main problem you find when using the radar to follow a possible target is the inaccuracy of the range readings, unless you are using a mod to improve these. The error can easily be more than 2 nautical miles, specially at long distances. This problem can be minimized with repeated readings at intervals of 15 minutes or more, with the added benefit of detecting any possible course changes of the target with time to correct your own course of action.
At the end of the approach phase you should have your submarine at a good position waiting for the target, with a pretty accurate estimation of its course but not a good speed estimation (you will have to work that out in the next phase).
This is a beginners tutorial, no previous knowledge is required, and since it is not about attacking techniques it doesn't matter whether you use auto or manual targeting.
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Enjoy