On a surface without any friction, a person would be able to jump only straight up. Any force which is applied parallel to the surface would cause the person to slip as there is no friction to push against him and keep him from falling over. Nobody will be able to make any sideways movement when all they can do is move up and down.
What could one do is lie on his or her’s back and take a deep breath, then stand up and jump into the air (which is a very tough jump under frictionless conditions). When one is in the air, blow out the air you earlier took in which will cause you to accelerate in the opposite direction. When you land, because there is no frictional you will keep that motion and continue to slide.