Navigation
About 80-90 percent of the races you will enter will have some kind of navigation or orienteering component. It's a bit intimidating at first, but once you start learning and have some successes, this is an aspect of the race that you will truly learn to love. And learning the basics is not all that hard. If I can (sorta) do it, anyone can.
Good navigating provides an incredible competitive advantage, and most experienced racers will admit that strategy, team tactics and navigation are a far bigger factor in their team's success than speed. That's why it's no surprise that athletes in their mid-40s are still winning the big events! Old age, treachery and good navigation will overcome youth and skill any day. So get out there with your map and compass and become the MVP on your team!
Training: First, buy a local topographical map, a compass and a beginning navigation book to get the basics. Next, attend a course or a camp with someone who is into "speed" navigation. Local orienteering clubs are a great source, as are adventure racing camps and clinics. Join a local orienteering club and start doing competitions. Try to do your first few with someone experienced, if possible, and watch their technique. Part of the efficiency of navigation revolves around where you keep your map/compass, how you hold and remember your location on the map, and how you access all of the information you need to get to the next checkpoint. The end goal here is to not only learn to navigate, but to navigate on the move. Tips: Buy several local topographical maps of your local area and take them with you everywhere you go. You can learn a lot just by being a passenger in a car and practicing terrain association with the map while driving around. You should also do occasional runs with your map and see if you can identify the terrain features as you go. Find a way to have easy access to your maps during all events. For hiking, get a map holder that hangs around your neck. For paddling, find a waterproof map case that you can secure directly in front of you and a marine-type compass that sticks to the hull of the boat. For mountain biking, create a map platform that's positioned across your handlebars. Make sure that your teammates have at least a rudimentary knowledge of navigation so that they can back your up or cover for you. The best case scenario is to have at least two capable navigators on every team. If you can find out the "scale" of the maps for your race course in advance (most will be 1:7,500 or 1:24,000), practice with maps of similar scale to get a feel for how far apart or close things really are. Mountain Biking
Most people considering an adventure race are pretty familiar with mountain biking and what it takes to train for it, so I won't spend a lot of time here. I'll just cover a few tips that are adventure-racing specific:
Tips: For sections that are certain to be at night, go big with the lights if the course is remotely technical. The extra weight will be worth the increased speed and safety. We use Niterider's newest HID light, which gives us the option of both super bright halogen for the sketchy stuff and a battery-saving set of L.E.D lights for the roads. Rig two bikes with towlines and all bikes with small hooks to receive a tow. We've had great success using retractable dog leashes (for small dogs) as towlines. Just cut off the latch at the end, tie the end of the line into a three-inch to four-inch circle that fits over the receiving hook on your bike(s), and zip tie the leash casing under your seat and around your seat tube. Voila! This is called the "Rocky" system, since my buddy Isaac Wilson's Jack Russell sacrificed his leash for our initial test run of this system for the last Eco-Challenge. Try to use the same pedal system as your teammates in case you need to swap bikes or bits of bikes for some reason. Buy/make a system for easy access to your food at all times. You will probably not be stopping to eat, and not eating on a mountain bike leg is not an option. I use a "Bento Box" rigged on my cross tube. 
