Wilhelm,
IIRC when you are playing stock, contacts will sometimes show up on the navigation map before you are actually within visual range of them. Which means that trying to locate them with the periscope or with binocs on the surface will not help. (Even if they are within the max visual range, and visibility is limited due to time of day/weather/etc. you might still have the same problem.)
So what you have to do is "follow" the contact on the map to get an idea of its general course, and then plot a course for your sub that will bring you close enough to it to see it and/or attack it if you decide to do so.
If you can figure out the general course of the contact you can get closer to it faster by running on the surface, however until it's within your visual range you can keep track of it with the the hydrophone (which will pick up contacts via sound that you may not be close enough to see).
You can do this by either staying submerged and paying attention to the bearing of the contact continually, IF you are pretty sure it's moving slow enough that you can intercept it or catch up to it running at your max submerged speed. Or you can run on the surface and then submerge every so often to 30 m or so and do a hydrophone check to see where it is and then surface again, adjust your course if need be, and take off towards the contact again.
I hope that helps, I'm sure other more experienced players will have more and better suggestions!
