Along with just going out and trying a race, pick up a book on the subject for some good base knowledge. Ned "The Lung" Overend has a book titled "Mountain Bike Like A Champion". It's got a lot of helpful information on racing and training.
If you're serious about your training, you'll probably want to get a heart rate monitor... so you will know when to ride hard and when you'll need to allow your body to recover. Ned'll tell you more on that later.
Keep your eyes on the local event calendars, for your area, pick a race and check it out. Either race it, or just go to see what it smells like up close. See if there are any clubs around your area that race/train. Talk to the guys at your LBS.
You said "I didn't know where to start"... You give them some money, they give you a number( hopefully a t-shirt), and tell you where to start. There's usually a banner overhead. Don't worry if you get nervous, chances are the guy next to you has the butterflies in his stomach, too.
;)
Racing's a blast!
Posted by ZG a 33 year old Cross-Country Rider riding a Sugar 2 & an R F X from Sherman Oaks on 10/22/02