Airborne Pass skill is a hardone. Basically jump with opponent and overtake him right after the jump. Best watch the short tutorial video for that:
You can also do it easily in Blizzard Mountain 'Snow Park Cross Country Circuit' if you have the Blizzard Mountain DLC.
Speed Boost skill can only be done when you have HotWheels DLC. Basically you can just drive around to get speed boosts by the boost pads around the map.