There is an excellent intoduction to Cyclo-cross on the British Cycling Website

Why cyclo-cross?
Cyclo-cross is a good form of winter training. You can never train at the same intensity.
You learn bike handling skills, riding safely in a bunch, and importantly falling off in mud doesn't hurt as much as tarmac!
There is a good deal of camaraderie as the weather in autumn and winter can be challenging!
Finally it also an excuse to get another bike? If you need one!
Skills to practice
To get the best out of cyclo-cross you need to practice getting on and off your bike quickly. There are obstacles or steep banks that may be un-rideable.
Practice riding off camber sections off-road and getting off your bike before you stall up a hill.
How do I get into cyclo-cross?
Equipment:What do I need?
Either a cyclo-cross bike or a mountain bike. Mountain bikes are a good place to start and if you get really into it you can splash out on a cyclo-cross bike.
Cyclo-cross bikes tend to be quicker than mountain bikes as you are in more of a "race position".
A cyclo-cross bike differs from a road bike, the frames are a bit shorter, bottom brackets higher off the ground, and the forks are wider to accomodate the fatter tyres. The gearing will be different and the brakes tend to be cantilevered to give the best mud clearance.
A helmet is mandatory when riding on the course, either in warm up laps or in the race.
On race day
All the CXNE races are "pay on the day", the National events need pre-entering (worth doing the ones nearby as they are fantastic for the atmosphere).
Arrive an hour before your race to sign on, pay and get your number.
Have a look at the course, if there is no race on you may ride the course but if there is a race in progress please stay off the course.
15 minutes before the start have that last drink/gel and make your way to the start line.
The starts are massed starts, but are often "gridded" with the faster riders off at the front.
There is a race briefing by the Commissaire and the race is started by a whistle/gun.
If you have never done a 'cross race before, you may be surprised at the sprint start. This is done by riders eager to get to the first obstacles before anyone else, as it can get congested on the first lap.
Don't worry about being lapped or being left on your own, you will quickly find riders of the same ability to battle it out with.
The races run for a set time length with the leader being given the bell on the last lap, once you hear that you know you have one more to go.