If you want to install a new drive into your computer it's pretty simple as long as you have the right cables from your power supply.
You simply buy an internal drive, screw it in place (probably next to your current hard drive), and then plug it in.
If you have an old computer it's probably using IDE which is a type of hard drive that uses ribbon cables (like floppy drives so). IDE drives also take 4-pin molex power connections.
Newer computers will be able to take SATA drives, which uses a small (and normally red or black) cable for data, and a small cable for power.
What make and model computer are you using? I'll be able to tell you what you're compatible with and then how to install it..