Some trainers have landing gear that is well.. crap. Make sure that the nose gear is straight, and then adjust it so that there is very little travel on the nosegear. Most of the time what happens is that we tend to overcontrol when trying to steer the plane. Add to this the speed needed to take off and the plane usually ends of veering off the runway. Your best bet is to cut power, abort the takeoff, and try again. I would try adjusting the landing gear before making any thrust changes to the engine.