It's a very common problem and not that hard to fix actually. The hardest part is getting your gamecube open.
First, you need a gamebit driver. If you don't have one, you can make one. You need a pen made out of hard plastic (try bending the pen--if it doesn't give way, it'll probably work). Melt the tip (don't burn it) and hold it over one of the four screws holding the cover on. After it cools, you should be able to open up your GC with it.
Unscrew everything and take out the main disk drive. Flip it over (be careful not to scratch the lens) and then unscrew the bottom. You'll then see a small black square with a screw on it. This adjusts the laser. Turn it about 30 degrees counterclockwise. Put everything back together and it should work. If it doesn't, turn the screw slightly more.