OK, so you have your old laptop and now you have to remove the warranty seal and take off all the screws. Look at the front panel, there may be some pieces of plastic covering some of the screws. I really can't go through disassembling it because it may be different for each type of laptop, BUT, keep in mind that you have to be very CAREFUL! Just some simple tips from the top of my head:
1) Remove the battery;
2) Don't touch the circuit with your hand or with the tools: you can manipulate these parts by grabbing them by the sides;
3) Be sure that you are not "electrically charged": statics can damage your LCD panel and other components that you may want to use;
4) Remember: there is always a hidden screw, so double check that you remove them all;
5) I SAID DON'T TOUCH THE CIRCUIT!
There also some parts that you still can use, like the hard drive! You can use it as a External HD for backup, but you need some hardware that interfaces the HD and the USB. Mine is a SATA/USB interface. Hopefully I'll make another Instructable for this.
Now, you can look behind of your LCD panel and see the MODEL NUMBER. You will need this number so you can buy the correct CONTROLLER BOARD. This piece of hardware does all the magic and turns your useless LCD panel into a real monitor.
Dealing with Statics (Credits: TCSC4 and Tazmjm69):
1) Use an anti-static mat and/or an anti-static wrist strap;
2) Use your PC cabinet: have it perched on your work bench and keep touching the grounded metal case every few seconds or even lean on it as you work.