When you're riding motorcross, you will hear the term "Ride your own race" many times again and again. It means, watch yourself and ride for yourself and if everyone keep themselves safe and aware, then there should be no problems on the motorcross track.
A lot of safety basics are commonsense, such as wearing your safety gear. No one with a working brain would get on a motorcross bike and race without proper safety gear. The same goes for when you're riding in a motorcross race. You want to keep your eyes ahead and always look in front of you, so you know if a hill, jump or turn is coming and if you need to watch out for another rider.
Don't look to the side to see how far ahead of someone else you are, a split second of taking your eyes from watching in front of you can cause an accident. Warm up on the track if you can pre-race. Some tracks will allow this, others will not.
Having good riding skills is another safety factor when racing motorcross. Practice, practice practice is the key to being a great racer. Superstars such as Chad Reed and Jeremy McGrath spent hours every single day honing their racing skills and if you want to be a great racer, you will have to do the same. You can't learn good skills from any book, movie or even article, although you can get some great pointers to try out yourself.
Another great way to insure your safety when motorcross racing is to ask a more experienced rider what they've encountered on a particular track. Most other motorcross riders are happy to share information about track terrain and conditions. Keep practicing, keep riding, and keep safety in the forefront of your mind when you ride and your motorcross racing times will be a blast!