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.
Step 2: Remove the Battery
Remove the screws and put them into the second slot in the ice cube tray.
Step 3: Remove the Motherboard to I/O Cable
Step 4: Remove the Cooling System
First remove the five black screws, and place them in the next ice cube tray slot.
Next remove the two silver screws, and place them in the next ice cube tray slot.
The cooling system will be stuck down slightly to the CPU. take your fingernail and hook it under the leftmost black screw hole and lift slowly and gently. Be particularly careful while pulling the cooling system off of the CPU.
Step 5: Remove the I/O Board
Take a small flat-head screwdriver and push the white part of the connector to the right out of it's beige socket.
Remove the single screw, and place it in the next slot in the ice cube tray.
Lift the blue I/O board from the left edge and it should slide right out.
Step 6: Disconnect the Keyboard Ribbon Cable
Use your fingernail to gently push the beige tabs downwards towards the battery. They should slide out approximately 1mm freeing the keyboard ribbon cable.
Step 7: Disconnect the Monitor Cable
Use a fingernail to push the tabs towards the top of the laptop and release the monitor cable.
Step 8: Antenna Cable Removal
Use your fingernails to lift the small gold connector away from the wireless card connectors.
Go ahead and disconnect the speaker connector. Take a small flat-head screwdriver and push the white part of the connector to the left out of it's beige socket.
Step 9: Mouse Ribbon Cable
Be particularly careful with this kind of connector as they sometimes will break off.
Step 10: Remove Motherboard Screw
Step 11: Lift Out the Battery and Motherboard
If something feels like it's holding the motherboard back DO NOT FORCE IT. Look for a screw or a connector you missed.
The battery disconnects from the motherboard with a connector that swings up.
Step 12: Remove the Speakers
Removing the speakers is a pain because they're held down with double sided tape.
Using a flat head screwdriver pry the edge of the speaker up from the bottom edge first. Slowly work the flat head screwdriver up towards the keyboard and the speaker will pop off.
Remove both speakers. Note that the speakers are marked L & R. When you're putting the laptop back together make sure they go in the right locations.
Step 13: Reveal the Keyboard
Peel the plastic backing off of the keyboard.
Step 14: Remove the Keyboard!
There are about twenty one tiny screws holding the keyboard in place. Make sure you use the right size Phillips head screwdriver. If you manage to strip one of these screws it will be hard to find a replacement. Put the screws in the ice cube tray.
After you remove the screws gently lift the keyboard away from the laptop body. If there's any resistance look for a screw you missed.
Step 15: Install New Keyboard and Put Everything Back Together
You should also check the model numbers of the old and new keyboards to make sure that they match.
Reassemble the laptop by reversing the steps that we used to take it apart!
If you have any questions or need a picture of a specific thing please leave a comment!