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Push very hard on the screwdriver and turn slowly.

ditto. I've experienced some very minor damage to one of my screwheads from not doing this, but luckily it still worked out and I didn't make the same mistake with any of the others.

Don't try to turn too fast.
 
Yah, i noticed there are a lot of non-mechanically inclined people stripping screws and drivers on here.
 
As said above, you must push hard and turn slowly. Your instinct (or at least mine) will tell you not to push hard, because it's an expensive and not-all-that-rugged machine, but it's the best way to do it.
 
I had no problem whatsoever. Granted, you need a VERY small screwdriver (eyeglass repair sized phillips head), but it's not a difficult procedure by any means.
 
Note that the screws aren't straight up and down- they lean over a little bit. (because of the tapered edge)
 
It's not 00 it's 0. I was having a very hard time with glasses size screw drivers but once I got this a real screwdriver with this size it was actually quite easy.
 
As an alternative, you could try a small flathead screwdriver. That way if you ruin one of the slots, you've got another one to ruin as well before the screw is totally "screwed." ;)

In all seriousness though, I do this all the time.
 
Where can you buy an extra set of screws for the mid-2009 MBP 17?

If I ever need to open the case up, I want an extra set right there in case any screws are stripped. Otherwise I'd have to order a new set, and wait with a inoperative computer.
 
I just want to say I feel for you. I did the exact same thing. Within three hours of owning my MBP, I had scratched the bottom case after pushing hard and turning the screwdriver and slipping. Grrrr.... That aluminum really scratches easily.
 
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