All you'll need to do to fix a GBC with stuff buttons is open it up (requires a tri wing screwdriver, $2 from eBay), clean the button pads with a q-tip and alcohol.
The pads in question are the black bits on the back of the rubber immediately underneath the button, as well as the circular copper traces on the board that the black bits come into contact with when you depress the button.
You might need 3 or 4 q-tips. You'll know when you're done because the q-tips will stop turning black.
Takes 10 minutes overall and is only slightly more technical than wiping your arse! Don't be intimidated!
No soldering required to get you back up and running.
As for your buttons, you can buy new rubber membranes that make contact with the board to register the press. Give the board a good clean with isopropyl and pop some new membranes in and your buttons will no doubt be good as new—no soldering needed!
If you're deathly afraid of making mistakes, get a desoldering iron. If you mess up just suck the solder up, reapply a bit of flux as necessary, and try again.