The first thing, you should actually verify that you do have a cassette, ond not a freewheel. Sheldon Brown's site is good here, providing photos etc.. My answer will assume that you are actually running with a cassette.
The outside of a wheel is called a rim. The centre is called a hub. On your bike, bolted on to the side of the hub is something called a freehub body. This part holds the cassette in place (and provides the freewheel mechanism).
The thing is, different manufacturers use different patterns to keep the csassette in place, so if you're buying a new wheel you need to make sure you buy one with the correct freehub body, or be prepared to fit one yourself (added faff, more tools). So that's why we can't fully answer your question.
However, what we can say is that 700x23 is enough to define the size of new wheel you'll need. This is actually the tyre size, but the two are pretty much interchangeable in terms of defining wheel size. Also, you need to make sure that you get something compaztible with your 7-speed cassette.
In terms of actually swappuing the wheel out, new wheels generally come with freehub bodies ready to ride, but don't come with cassettes. So your problem basically becomes one of getting the cassette off the old wheel to use on the new. To get the cassette off, you'll need something called a lockring removal tool, which is basically a keyed nut, but again these vary with cassette manufacturer, aqmongst other things. Park Tools, among others, offer a good selection here.Then you'll need a spanner, 1" iirc, and lastly something - a vise or a chain whip - to keep the freewheel still while you unscrew everything. You'll use the same lockring tool/spanner to tighten it all up again. It really is a 2-minute job, but without the correct tools is quite impossible.