I have several external drives, accumulated over years. My most recent one happened as a result of one PC dying. It seems to be beyond repair, so I took out its hard drive and housed it in a USB enclosure.
You can go one of 2 routes, enclosure + OEM HDD (take your pick, as long as the enclosure supports it) or dedicated external drive. Obviously it's easier to go buy a WD MyBook than to scope out competent enclosures, drives, and then assemble the components. That's up to you. The market for external drives has increased notably, so there are good options either way. If you go the enclosure route, get one that supports the drive type and size you intend to get for it, and that it supports the best possible internal data speed for that drive. [Example: UDMA 6 for UATA drives.] You also want it to support USB 2.0, and if you can use it, firewire. Now there's a firewire 800 too, with the old standby now being dubbed firewire 400. That's Mbps, as in bits, not bytes. If your motherboard supports it (doubt it), there's also a new 3Gbps eSATA standard. WD makes some externals which support it.
USB 2.0 gives you 480 Mbps, or 60 MB/sec. Standard firewire is 400 (50 MB/s) but it is said to provide better sustained rates. These numbers are roughly the best throughput you're likely to see out of a UATA drive. SATA, though, is a good deal faster. I don't know what you have right now.
An enclosure consists of the case, an interface to a normal drive's power and data plugs on one side, and USB or whatever else you opt for on the other. You install the drive in the little case, plug in the cables, close it up, attach the AC power and external connection cable, and you're good to go. At this point you can partition it and format it.
Once the drive is performing to your satisfaction, you can go into device manager and optimize it for performance. By default, Windows does not cache external drives, so you can unplug them at any time without risk of data loss. I've been having Windows cache all my externals for years, and I have yet to lose one byte because of it. The performance is markedly improved by this, as you might imagine.
I think I'll stop here for now. If you look at my "Help! dead computer" (or similar) thread, I get into a discussion about some techie details, if you care. I don't think it's necessary.