General

For something that minor on a large amount of consoles, you might see if there is a video game store near you.

Rubbing alcohol on the contacts and back of button likely could fix it if not a bigger issue. You'd likely need to buy the right screwdriver (tri-tip maybe, otherwise glasses/jewelers phillips likely, both cheap online). As Pork said, watch a YouTube video or two and see if you're moderately comfortable. Many common repairs are pretty simple with decent YouTube instruction, and the more you try the more capable you become! Remember, you can't make what's broke to you more broken. And lastly...

"If the women don't find you handsome, they should at least find you handy."

I highly recommend what KCPenguins said. Look up a YouTube tutorial. I did this in order to tinker with a DS.