Oh. Plugging it into the desktop should be straightforward.
You need a SATA cable and a free SATA power cable inside the machine. (They are thinner than the normal large 4 pin power connectors, usually black in color but not always).
Edit by Mez: Edited again: removed my comments, CK9 didn't give the correct description of what he wanted to do
Plug the SATA cable into the hard drive and into a connector on the motherboard (it only goes in one way, don't worry about orientation). The connectors on the board might be labeled something like "SATA 0" through "SATA 3" or something like that, it shouldn't matter which one you use.
Mount the drive into the drive bay (sorry, can't really get any more generic than that, since all cases are different, you'll have to figure out how to do that).
Boot the computer, the drive should be recognized right away. (If not, you need to make sure SATA AHCI drivers are installed for the SATA controller on the motherboard. If your other hard drive is SATA, this shouldn't be a problem).
This is preferable to using a USB cable to connect the drive to the desktop machine (unless your desktop doesn't have SATA or something), since you will get -much- improved transfer speeds (Maximum of 3 Gbit / sec vs 480 Mbit / sec, though the drive probably cannot deliver anywhere near the 3Gbit max).
As far as actually using this USB cable. Is it an actual enclosure? Or just some sort of adapter cable (not familiar with the adapter cables, just enclosures). You can plug it into the power supply connector from the computer as mentioned above. If you don't have a SATA power connector (it's the larger of the 2 connectors on the hard drive), you will need an adapter to go from the regular 4 pin to the SATA connector.
Generally the USB side of things should not require any kind of drivers or software installed on the host machine. This is true for enclosures at least. It will appear as a USB mass storage device to the OS (basically, if flash drives work, which are another kind of mass storage device, then the hard drive should work as well).