If it's a shopkeeper or king, you can use the T key (IIRC), which stands for Transact.

Other characters can't be interacted with that way. Some may say something when they get near (or even do things like steal things), and you can attack such characters if you want (and, in fact, you have to do this at some point to complete the game), but there's no talking to random townspeople in this game; that didn't come until Ultima 2.