Hi Beren,
You'll need to open up your case and work out if it's got any free drive bays as some store bought computer tower's only come with 1 space, check your motherboard has a spare SATA port and a spare power cable for the hard drive. If it does then brilliant. You'll need to buy an Internal HDD (usually 3.5" for desktops but again check inside your case) and you'll need a SATA cable too to connect it to the motherboard.
You can also get external hard drives which use a USB port, easier to setup but not ideal if you're wanting to use it as permanent storage as internal SATA is faster.