So.. How do you normally do it? Taking pictures of ppl on the street. Do you approach them after you have taken the picture? Have you ever been told not to take pictures of them? Sorry if I don't make any sense..
Simple answer: just press the shutter. Nothing else is needed, Esbjorn! Of course as always: you may talk to the people or not; their and your choice. As for being apprehensive: forget about it and just press the shutter, please.
I think you have to develop your own approach. Just get out there and take pictures and see what works for you. Some street shooters are more "aggressive" and others are more "laid back." You have to figure out the best way for YOU to get the kinds of pictures your looking for and the only way to to it is by hitting the streets with a camera. Good luck!
I'm just starting and have the usual qualms. Reading the piece Umut recommended (which is indeed helpful), it occurred to me that part of the answer is to be a tourist, "just trying to capture the spirit of (name that town) for the folks back home."