making a new chair seat

Hi. I have a question. I recently bought a chair on clearance. It is beautiful wood, but the seat was missing. I made a new seat board from 3/4 inch plywood. I upholstered the board and it looks great. Now I want to screw the seat to the chair. I don't know if I should drill the holes so they go all the way through the seat board or if they should only go so deep into the wood. If they go all the way through will the screws poke up through the seat cushion? Help.