Under an access panel: Many laptop designers situate their hard drives under a removable panel located on the bottom of the machine. Remove the panel; detach any retaining clips, screws, or frames; and slide the drive out. Usually, you'll have to pull backward to free the drive from its connector, and then lift the drive up and out.
Under the keyboard or motherboard: On laptops where the hard drive is located in one of these places, your job is a lot tougher. Carefully store the removed parts in a logical, organized manner, however, and you'll find the task time-consuming but not impossible.
Though the particulars vary, the disassembly procedure should go something like this:
Flip the laptop over and remove the screws that hold the keyboard deck in place. Remove the keyboard deck. This may require sliding a spudger along the seam between the lower portion of the case and keyboard deck to release snaps that may be holding the two together. Some modern units are sealed, so don't assume that there's an easy way in. If you discover that your laptop vendor used hot glue to hold things together, you might want to farm out the chore--it's easy to mess things up with heat. Remove the keyboard and other components that hide the hard drive or prevent you from dislodging the motherboard. This step may involve taking out screws; peeling back tape; detaching components such as modems and Wi-Fi modules; and detaching clamped ribbon cables, regular cables, or antennas with pressure-fit connectors. You may also have to remove metal RF shields. Be gentle and reread the section on hazards, above. If the hard drive is situated under the motherboard, you can probably remove the latter after taking out a few more screws. However, the ports integrated onto the motherboard protrude out the case, so you may have to jockey the motherboard as you pull it out. Again, be alert for hidden cables.
Stop the disassembly process as soon as you have access to the hard drive. I've seen drives that were taped in place, screwed down, or held in position by fancy hardware. I've also encountered drives that lay loose after I removed a shield or panel. None of these various circumstances pose a special challenge; but carefully observe what's there, and above all don't force things.
Once you've successfully removed your old hard drive, simply reverse the procedure to insert the new drive and reassemble the laptop. Enjoy your rehabilitated laptop!
Of related interest: How to Add RAM to Your Laptop