Every stranger-on-the-street will have his or her idea of how to respond to your idea. One person may ask for payment, acknowledgement of their time and effort, their real name or a nom-de-plume and even a print. Others, particularly students, can be gregariously accommodating (sometimes too much so!). Choose subjects carefully.
I have photographed a few people recently, including a part-time model who played the role of a Goth in a graveyard for Worldwide Pinhole Photography Day. I met her just by pulling her up on the street; turns out she is also a photographer and we bounced a few ideas around (this mutual collaboration is valuable if you find somebody to photograph and the result is quite successful). Post-shoot, Lady Sarah was given small machine print of each of the seven shots, and requested nothing more.
Maybe carry with you a small album of works you have completed relating to photographing people. I think in this modern, technology-driven and socially-aware age most people will agree to a photo if you explain it to them. Having an engaging and enthusiastic personality will definitely help, as will knowing how to back off from those who simply "are not amused" by your angle, however well-meaning.