Any tips on how to improvise in acting?

Never say "No" to a premise set up by a fellow actor, unless the "no" leads to a bigger choice. Never block your own thoughts. Dont always go for the punchline, help set it up as well. Dont think of rehearsal games as excellent ideas for performance... and read Impro: Improvisation and the Theatre by Keith Johnstone. Research the big troupes all the way back to commedia Most important: Listen. everyone else mentioned excellent ideas as well...

Improvisation is about giving and accepting offers. It would really depend on who you are working with, but improvisation is really building on what you currently have. As long as it sticks to the current situation and if you have a set role, it fits the role, say it. Sometimes you need to go with the flow. When acting, try to bring the topic back in so your lines come back into play. Some lines cannot be avoided or meaning is lost. So try not to end up in that situation when doing any polished performances, but if improvisation is the intention, yeah, go with my ideas. I am an actor myself, or at least studying it.

Well, first of all, you need to know the character inside and out. Try asking yourself random questions about the character. I always find these are helpful when im doing everyday things, like eating breakfast, for example. When no-one is around, ask yourself, how would the character do this? Then, transform yourself for a while. This should familiarise you with the character. Now, if you just freeze on stage, work on what has already happened in the script. If your character has just had an argument, perhaps you could use little body language or storm off. But the rest of the cast with you should have mutual respect and confidence with you. With a discreet alarmed twinkle or flutter of the eyes, they should know to help you out, and bring you to a point in the script that you feel comfortable with again.

Well when you are almost running out of things to say, talk slowly to give you some time to think of something, the audience will think it's all part of the act. :)