Shaking cocktails without bar equipment
I've been able to shake and strain cocktails with two cups pretty easily.  Ideally one cup should be slightly smaller than the other, though this isn't absolutely necessary if you're careful.

Put the open ends together and shake as necessary (if they're slightly different sizes as described, you can get a real nice seal and shake vigorously).  Now, place one cup on the counter, and the other on top of it upside down, ideally still "inside" the other one.  

You want to tilt the top cup about 5-10 degrees to the side, which will "break the seal" between the two cups and leave a very small opening.  That's where you'll strain through.  Now all you have to do is tilt the entire contraption 90 degrees and pour!

This is more easily explained with images...I will try to find or make one for you ASAP.

edit: Couldn't find a good example, so made one for you with what I found around the office: