So, to begin, let me first repeat that this fix will only work for an XBOX with a Liteon DVD drive - you can tell your DVD drive manufacturer by looking at the disc tray. Check this site out:
Scroll down to find a picture comparing all the drives. If you happen to have a BenQ drive, the tray will look the same as a Liteon. You can tell the difference by reading the big sticker on top of the drive (which will be visible when you open up the XBOX).
Be aware that an "Open Tray" being displayed in the dash could also be the fault of a dying laser. Luckily, this fix is free, and if you continue to have issues after you have done it, the next logical step would be to replace the laser.
Keeping this issue from recurring will require modification to a component of the DVD drive. If you are uncomfortable with doing this, you CAN still get your drive to work by simply moving the laser. However, the constant "Open Tray" message will most likely come back after awhile. More on this later.
I also want to say that this will ABSOLUTELY VOID YOUR WARRANTY. Check on xbox.com to make sure that your standard warranty is up before you crack open your box to perform this fix. Alright, with all that out of the way, lets get it done.