I personally wouldn't try to guess what they would ask you to do. Sure this allows you to think longer about what you would do, but it defeats the purpose of improv! Improvisation is supposed to be spur of the moment comedy. You have to think on your feet and be committed to your idea. Here are some tips:
When practicing miming/improvisation, think about something that you would do in your everyday life. Going to get the mail, walking your dog, playing with your cat, doing homework, etc. Whatever you want really. (When you advance, having someone else tell you a scene is good practice.) Then act as if you are trying to tell someone else your experience without being able to talk. Once you have this down, try to come up with something that would be funny in the story. Maybe you are walking your dog when s/he sees a cat and starts to drag you along. Use every part of your body to portray what is going on and try to make it easy for the other invisible person to understand. Don't think that you are being silly! Being silly is the whole point!
Doing it in front of others when you are comfortable helps A LOT. Having them play with you is even more helpful. If you can, gather friends for a night of charades or a similar game. This allows you to figure out how to portray an idea/story without speaking. The best tip I can give you is to think of an idea and commit to it 100%. Do not be afraid to change the story as you go, just as long as you keep the general idea. (i.e. walking your dog.) Do your best to make the other people understand what you are doing!
I hope this helps, I took classes on mime and improv for several years and HIGHLY recommend taking some. It not only helps with a situation like this, but in being an outgoing person in general!