Always wear safety gear: Helmet, knee/elbow/wrist pads. The helmet shout fit snuggly without being too tight. Your helmet should meet the standards set by ANSI, ASTM, CPSC or EN1078. Seriously, where safety gear. It's alot cheaper and less painful to replace gear.
Make sure to give you board a thorough safety check before riding. Check all nuts and bolts often to make sure they are tight. This includes nuts and bolts fascening the trucks to the deck, as well as wheel and kingpin nuts. Be sure to how to adjust your trucks before doing so. A tighter kingpin means more stable, while a looser kingpin nut yields better carving. When learning be sure to tighten your kingpin nut for a stable ride.
Be well aware of traffic and traffic signals in areas where you skate. Also have a good understand of how you're going to stop if needed. Don't start if you're not sure how to stop. More importantly, know your limits and skate within them. It is also important to understand the limitations of those around you. Respect others, and be considerate of younger/less experienced riders.
Always have a game plan in case of an emergency. It sounds basic, but ask yourself when you skate (especially in a new place) "what would happen if an accident occured?" It may be as simple as understanding where the nearest hospital is...or remembering 911 if needed. Accidents do happen, but if you take special care to plan ahead, you can prevent serious problems. It's smart to carry a phone and ID while skating.