What I (as a very shy person indeed) try to remember is that if the other person is alone they probably want somebody to talk to. Even when I've been to events with my wife, the both of us really want to find others to talk with. Some of the time I don't end up getting the courage up to talk to strangers but sometimes I do, which just helps build my confidence up for the next time.

The other big tip is always "Fake it til you make it". I just try to think of what somebody who's good with people will do then try to do that. The other person doesn't know you have a hard time with strangers, pretending can help move you a little ways forward.