Adding a hard disk is a simple task for just about anyone... Open your case, slide it into the ribbon (red line facing the power cable), slide it into the "holding bay" and power up... However, identifying your hard disk type and how many you can have could be another issue entirely...
Your system should support any capacity hard disk, so it's simply a matter of identification; the easiest route is to simply Google your motherboard version (and it should be in a huge font on your motherboard, as all manufacturers proudly want to spam their product).
If you can't find the model on the motherboard you're not at a loss, you can identify most times by the adapter... There are two main types of connector, IDE (which is a bulky 40 pin adapter) and SATA (which is a smaller adapter which you shouldn't even really be able to identify any pin's). From here you'll need to see if you're dealing with SATA or SATA3g; it should list it on the motherboard itself, all else fails however, you could just go with a standard sata hard drive.
So, from here, just head over to the Hard Drive section of NewEgg.com and select a "system type" (Desktop), Connector Type (SATA, SATA3g, IDE, etc). I do NOT recommend selecting a capacity however, you'll often find a much larger hard disk for the SAME target price, so it's good to shop around.
After you hit search, select "Most Reviews" from the "Sort" box to the right; this will allow you to rely on other peoples reviews of products (always best to buy what's reliable right?). From here, identify a disk you want (size, rating, etc) and read the first set of reviews; if it looks good to you, then buy!
As I said before, you'll find prices very low for some, semi high for others, it's up to you with what your needs are.
There are also External Hard Drives which come with their own USB or FireWire enclosure, if you don't know what ports you have on your machine, you can usually just default to USB (as all else fails, you can just buy a USB hub if all of your ports are full). The link to the NewEgg.com External Hard Drive page is here. You can also make your own external hard drive, but that's a topic for another article.
Note - As SATA3g and ATA133 are backwards compatible with their predecessors, you should have no problem putting them into a system as they will be read regardless of their faster specs. However, SATA and ATA themselves are NOT the same types of drive, thus you cannot put an ATA drive into an SATA slot (it wouldn't fit in the first place).