Take a look at the platformer-demo, especially Actor.gd and Player.gd. The idea is not different from other movement: you move the character each frame along a velocity-vector, so if you want your character to fall down, you just have to change the orientation of that vector. It's usually done by adding a certain weight (the gravity) to the y-direction of your velocity-vector each frame, so the character will fall faster and faster the longer it is in free fall.