ok...don't panic. you can do this.
run down to the harware store and pick up an IRWIN screw extractor set. the set I have came with 5 spiral extractors, it should run you about $15. pick up a T-Handle as well, like the kind you use on a tap - should be near where the taps & dies are in the store.
you will also need a spring-loaded center punch and a GOOD drill bit set with 64th/inch graduations.
first, you will need to use the center punch to make a divot in the center of the damaged screw. (so the drill bit doesn't walk)
then, pick an extractor from the kit that looks about right. you want to make a hole that is about 1/2 the diameter of the screw. the kit should refer you to the appropriate sized hole to drill. be careful to drill the hole straight on and as close to the center as you can get. try not to damage the threads on the hole that the screw goes into. make sure you don't break the drill bit either, or you will have a large unsightly bruise from smacking yourself in the head.
once you have drilled out the center of the damaged screw,
insert the extractor and tap lightly with a hammer until it seats.
the spiraled head of the extractor should grab the hole you just made and hold firmly so you can back the screw out.
next, attach the t-handle to the extractor and make a prayer/offering to your favorite diety and turn anti-clockwise. with any luck it should come out.
*this does not always work, but if you are very careful and take your time it should do the trick. please don't blame me if it doesn't - I'm just trying to help
GOOD LUCK! That extractor set will come in very handy in the future. You'll be glad you bought it!