All you can do is replace the disk drive. If its the first generation X-box then you would probably do better simply buying a new one. My box just died and it would cost 40-50 bucks to repair. Replacement now is $99 new.
You can clean video game discs with toothpaste. I have tried this method and it works. Or you can use a soft towel or piece of cloth to clean off the disc of any particles of dust or dirt.
There is a common Xbox 360 problem known as the "Red ring of death". It is possible that this is your problem. Microsoft will RMA your Xbox if this is what is going on, and send you a replacement one.
Go to Microsofts website and look up suggestions or even call them and they might be able to replace your Xbox. They replaced our 360 that was doing same thing.
There might be a smudge on the disk that you didn't see prior to putting it in,that could be causing it to not be able to read it. Try wiping the disk off gently clockwise with a babywipe to get any and all smudge/dirt off of it.
