Look at things like the tire pressure and make sure that the gears and the brakes are functioning properly. Those are the big things; the safety items. Make sure that when you grab the brakes, the brake is engaged and that the brake levers are not going all the way to the handlebar of the bike before it engages the rim. Check your tire pressure; again, on the side of your tire it always gives the recommended pressure. Follow those recommendations; pounds per square, anywhere from 30-50 psi are usually safe for mountain bikes. Most people, would put 40-45 pounds of pressure in their tires. If the pressure is not right, then you may get a flat. So check things like the gears and brakes. Make sure that it shifts when you want to shift gears and that there is nothing that can hurt you.
