Unless it is small enough to fit in your laptop (and I seriously doubt it.) you will need a special piece.
Like a external hard drive bay, or a cord that plugs from your drive to your new computers USB slot.
search for either a IDE to USB cord, or a SATA to USB cord depending on your drives connection.
There are two types of IDE, a small 2.5, and a regular 3.5 connection, so make sure you get the right one.
SATA hard drive to USB cord:
Or, I suggest you just find another desktop to plug it in and copy files to a thumb drive, or CD/DVD.
If you need a operating system to do so, put a Linux operating system thumb drive or CD into the computer you are plugging the drive into.