There are two main kinds of computer monitors: Cathode Ray Tube (CRT) monitors and Liquid Crystal Display (LCD) monitors. CRT monitors use hundreds of small electron guns to shoot electrons at a fluorescent screen, which emits light and creates images. LCD screens use properties of liquid crystals to modulate light and create images. In either case, taking apart the monitors is a relatively straightforward task that requires few tools and time. It's very important, however, that you take care to diffuse to ground the power stored in the capacitors, which can store thousands of volts of electricity even after the monitor has been turned off for days.
Take the monitor outdoors and place it on the ground, perhaps near some grass. Lay your lamp chord out so that the exposed leads go to the grass, which is where the charge from the capacitor is going to be discharged.
Take the back of the computer monitor from the front screen. Find any Phillips head screws holding the back to the front and unscrew these. There are usually a couple on the sides of the monitor and the front, but every model is different. Pry the back of the monitor off the front using the flat end of a flathead screwdriver.
Place the plug end of the lamp cord on the metal rods sticking out from the large suction cup, which is the capacitor, attached to the back of the display. Hold the plug against the metal rods for a moment. This action should discharge the stored voltage to ground.
Take apart any other parts you wish to, such as heat sink or CRT neck board by continuing to remove screws from each component or pulling off connecting plugs with your pliers. For example, pull off the four connecting plugs from the CRT neck board shield using the pliers and then unscrew the shield from the neck board and pull it off the unit.
Place your LCD monitor display side down. Remove any screws you see on the back of the monitor and near the monitor's stand.
Insert the head of a flat head screw driver between the two halves of the monitor, the front and back. Carefully slide the head through the gap, feeling for any plastic clips holding the two halves together. Depress these clips when you reach one. Do this until all the clips have been disengaged and the back of the monitor comes away from the front.
Unplug the cables from the sockets on the circuit boards and inner back panel revealed when you took off the back of the monitor. Remove anymore screws you see on the side of the inner back panel and pull it off of the front display screen.
Always ground your metal equipment to remove any static electricity if you wish to use your monitors again after you've dismantled them. Remove static electricity simply by pressing the tip of the tool, such as a screwdriver, to another metal object nearby.