Move all furniture out of the room.
Put on your work gloves, then remove the baseboard trim in the room. Insert the pry bar in between the wall and the trim near a nailing point and gently pull back slowly until it separates from the wall. Pulling back too quickly can cause the trim to snap and break. Use the same procedure to remove any trim around doors in the room as well.
Vacuum the floor. It's important to get any debris off the floor because otherwise it could get stuck in the sanding discs and gouge the floor.
Attach the 36-grit sandpaper to each of the sanding discs on the random orbital sander. The exact process varies from one sander to another, so follow the manufacturer's instructions.
Put on your safety goggles and dust mask, then plug in the sander.
Start in one corner of the room and turn on the sander, slowly moving it back and forth across the floor. You'll begin to see the wood lighten in color in the areas where you have sanded. While you don't have to follow a specific pattern with a random orbital sander, it's best to work from one side of the room to another so the entire floor gets evenly sanded.
Turn the sander off and remove the 36-grit sandpaper and attach the 50-grit sandpaper.
Turn the random orbital sander on and sand the entire floor, working your way from one side to the other, then turn off the sander.
Replace the 50-grit sandpaper with the 80-grit sandpaper. You'll need to make another pass over the floor with the sander to get the proper smoothness.