This information in this Instructable is specific to the Asus UX21E, but by reading my tips and following the general disassembly lessons you should be able to work on your own laptop.
That being said taking apart electronics has the potential to damage or destroy the electronics, so don't try to repair your own computer unless you know what you're doing.
You need a couple of supplies before you begin this process:
Screwdriver set with Torx bits
Ice Cube Tray
Step 1: Take the Back Cover Off
Do Not Use the Wrong Size or Type of Screw Driver!
Take out the eight short screws and put them into the first slot in the ice cube tray.
Now take out the two long screws and put them in the second slot in the ice cube tray.