Some manufacturers have instructions on how to take apart their laptops. For example, Dell has instructions for every single of its laptops. There are also unofficial websites, most notably
http://repair4laptop.org/ Most laptops can be taken apart without specific instructions, but there are some things that are helpful to know.
First of all, the key lies in knowing when you can apply brute force, and when you shouldn't. Saying that applying brute force is always wrong is, unfortunately, incorrect. If you misjudge it, you may damage the laptop. Most likely the damage will be cosmetic, but it will lower the computer's value.
First remove battery, RAM, hard drive, wireless card, PC card (dummy). All these can typically be removed relatively easily from the base of the laptop.
Notes:
battery may have a "lock" switch -- should be set to not locked
in rare cases hard drive(s) might be actually inside the laptop (Like Dell XPS M2010)
the hard drive will have a special connector on the end (sometimes the connector is on the motherboard, though). If the hard drive is IDE, when removing this connector, try to pull on it straight, without skewing it to one side, or some of the pins on the hard drive may bend (although it's not terrible, you can later straighten them back yourself)
WiFi card will have two tiny cables attached it -- antenna. Memorize which cable is attached where before disconnecting them.
Optical drive can usually be removed without taking the laptop apart. There likely is a single screw going through the back side of it. After you unscrew it, you can pull the drive out.
Make sure to unscrew every single screw on the bottom of the laptop. There may be screws inside the battery compartment.
Before trying to pull the laptop base apart, disconnect the keyboard:
There probably is a plastic part going above the keyboard, just below the LCD screen. Use a flat tool (flat screwdriver works) to push out both its ends, one on the left and one on the right. This plastic thing MUST be removed for the laptop to come apart. Here is where brute force is sometimes necessary. Below it are some screws that hold the keyboard in place.
Don't pull out keyboard too far -- it is connected to the motherboard. Pull it out a little, and disconnect. Below the keyboard there may be some additional screws that hold the laptop base together.
The display is connected to the motherboard via video cable, but it is also connected to the wireless card via antennae cables that were disconnected earlier. Pull out the antennae cables through the hole in the motherboard. Now you can disconnect the monitor altogether and put it aside.
Only now can you take apart the base of the laptop -- make sure you unscrewed all the screws and try to separate two halves of the base.
Notes:
sometimes screws are hidden! If the base does not come apart, look for manufacturer's markings near the screw holes. If you see a marking, but no hole -- there may be a screw covered with a sticker or something.
Sometimes screws require special screwdrivers. Make sure to remove those screws too. You can usually remove them with a small knife, or very small scissors if you don't have the right screwdriver.
One of the halves will contain the motherboard with stuff on it. Most likely you already can disconnect the modem and the video card. Sometimes you may already be able to disconnect everything else as well, but not always. There are screws holding the motherboard in place, some might be a bit hard to find (and some may NOT need to be unscrewed, as they connect stuff to the motherboard). When lifting the motherboard out, make sure that:
PC card release is pushed in. Sometimes it needs to be pushed even MORE in.
The VGA port may be additionally attached to the motherboard with two screws, whose tops are actually screw-holes for VGA cable screws! Use a tool to remove those. Pull out the motherboard from one side first (usually opposite to the PC card), then pull it from the front, then lift it. Careful, the motherboard may have additional invisible connections on the bottom.
Removing the fans and the heatsink is usually pretty easy. The CPU is likely locked to the socket. Use a flat screwdriver to unlock it, then lift it gently. The CPU pins are very easy to bend, so be careful.