First you need to find a hard drive. Look online for the best deals. Obviously you want to pick one with more gigabytes of storage space, but pay attention to rpm, too. That tells you how fast the hard drive spins. The faster the hard drive, the better some programs will work, especially if you spend a lot of time writing data to the hard drive.
I also recommend getting a hard-drive enclosure. That way you can clone your current drive, then you just put the cloned drive in the laptop and boot up. That's what I'm going to show you how to do. If you don't use an enclosure and don't want to buy one, you'll have to do a clean install of the operating system on a blank drive, then restore your data from a backup.
I'm going to tell you about the cloning method here. The procedure is pretty much the same for Mac or PC. First you need cloning software.
For Windows, I've got two options. Clonezilla is less prone to errors, but you have to burn it to CD and boot off it, rendering your PC unusable for anything else.
Macrium Reflect can image the drive while you're still using Windows. Just don't go changing significant amounts of data while it's running. Update Plenty of folks wrote in complaining that Macrium only makes an image but not a bootable clone of your drive. Try EASEUS for a freeware bit-for-bit cloning piece of software.
For Macs, Carbon Copy Cloner from Bombich software is super easy to use and clones the drive while OS X is running.
In both cases you're making a bootable copy of your current hard drive onto the new drive.
Next put the new drive in its enclosure and plug it into the laptop. Launch your preferred program, or boot from the CD if you're using Clonezilla. Make sure you're making a bootable copy and start things off! This can take several hours for larger drives. My 300GB drive took 4.5 hours to image. Once you have the drive copied. You'll need to take out your old drive and put in the new one.
The procedure varies for different computers. I'll talk about two examples. We'll start with a Windows machine.
Make sure the computer is off and unplugged. Touch something metal to make sure you don't still carry a charge.
In the old ThinkPad T61 I have, the hard drive is in a slot on the side. You unscrew one screw and the carriage slides out. Almost all hard drives are in some sort of carriage. Unscrew the drive from the carriage, and put the new drive in, screw it back up, and put it in the machine. Then boot up.
It should start just like normal, but with a lot more space on the hard drive.
Now let's switch to a Mac. Again make sure it's unplugged and touch something metal to discharge any static electricity you carry.
On this 15-inch MacBook Pro, the hard drive is underneath. Slide the silver lever to open up the bottom compartment. Unscrew the holding screw and remove the bar. Then pull out the drive and unhook it from the connector. Instead of a carriage, the Macs have four Torx T6 screws, so you'll need a torx screwdriver. Unscrew those and then screw them into the new drive. Now hook the drive back up, and slide it in so the screws sit in the little gaps made for them. Then replace the bar and screw it back in. Close things up and again, it should boot just like normal!
Consult your laptop's manual for exact instructions, but this should give you an idea of how it goes.