Step 1: One Step Fix...or Not

So as you can see I got a cheap xbox. It had the open tray error, put in a disc...says "reading"...then says "open tray" no matter what disc you put in.
I simply cleaned it.

Not going into details on how to disassemble the xbox or the DVD drive, there are other threads dedicated to that.
Open up carefully, get lots of q-tips and clean clean clean! I used a dab of windex on a q-tip then applied to the laser lens, then again with a dry q-tip. I reassembled and BAM it worked!
While it was apart I gave the mobo, fan and heatsinks a cleaning as well.

Step 2: Other Crap That Will and Will Not Work

Reset DVD drive/recalibrate
Turn on Xbox by hitting eject button, immediately stop tray letting only open half way. Gently push the tray back. The tray will freeze momentarily and close by itself. Turn off console and turn back on. This shit didn't work for me but mine had a dirty lens, and this does seem to be a common fix.

DO NOT SWAP DRIVES.
If you don't know by now, drives have firmware built into them that match the motherboard of the console. There are ways to transfer the data or swap circuit boards though.

TAP IT
I've also read if you TAP the console in the general area of the DVD it will boot up. This apparently works on drives that are on the verge of going out and is only a temporary fix.

Make sweet love to it
Put on some Barry White, dim the lights, and lay that sexy DVD drive by the fire...

Hail Mary
This requires pantera or possibly some Ludacris at a high volume in the background. Tie a rope or bungee straps to the xbox, then secure it with a latchable hook.
Now disassemble your washing machine or buy a spare one. Mount the motor to a large surface out in the open that is secure, like a pool deck or weight bench in a prison yard. You'll need lots of feet of extension cord. Test the motor make sure it spins hard and fast. If you hard wired it correctly it will spin on high without a limiter. Now attach 7.8 feet of cable to the motor and attach to console latch. Stand 8.2 feet away and power it on. If you did all this and took video it would probably go viral and Xbox will donate a new one to you.