When sitting (front side downhill) pull your heel side edge as close as possible to your butt (more knee bend, how close are your calves to your thighs?) Dig the edge in hard as if you were carving. Lean your chest forward between your legs, including arms downhill of the board, so you center of gravity is close to over the board. Now stand UP with your legs. It's actually about flexibility more than strength. Your legs will be plenty strong if you have the starting position right.
You can practice this by sitting on the floor at home (no board, boots, snow pants, perfectly level floor) and just stand up without using your hands.
One nice thing about this way of standing up - if you slip you fall on your butt again instead of jamming your hand / wrist / arm.