I also plot the target on the nav map to check the crew estimates of course and speed, and help me set up my firing position.
Also, jgbishop, you only mention 2 observations of the target. That's enough to get a solution, but not to check it. And the crew's course/speed estimates can be off.
So, I would only add one thing to ridyard and keldunk: once the position keeper is on, you can look at it to see the bearing and range according to the solution in the TDC - it's small, but readable. Whenever you take a bearing/range observation look at how the solution in the tdc changed - I mean the bearing and the range. If the bearing is not what you expect, your course/speed are probably not right. For example: target heading east, you are heading north, target is on your left, say relative brng 320 and going to cross in front of you. After a few minutes the tdc says the target's rel. brng is now 325. If you put up the scope and the target is more to the right than expected, like at 330 instead of 325, your solution speed could be slower than target's actual speed. You could raise the speed a knot, check everything else in the tdc (reset the AOB to the course you think target is on), and check it again after a minute or two. Once your solution is such that the tdc's current bearing and the target's current bearing stay matched, it's good. (The bearing difference can also be caused by other things than speed errors, it could be that the range is off or the AOB is wrong. Use all your other data to make your best guess - observed AOB, crew's estimates, what you get on the nav map plot if you did it. But at least for me, it's usually a speed error, or combined course/speed error.)
Also, I never had much luck with the training missions. I remember SH3's torpedo training mission, with the cargo ship that suddenly started it's engines after you fired. I learned manual targetting by finding my first convoy in a career, saving the game, and trying my approach a few times until I got the torps to hit.
Keep trying. I was really frustrated at first, but when I got my first hit, I was so excited I wanted to tell everyone. But no one around me cared.