Originally Posted by management
No I'm not using that. I'm using a huge and mighty heavy random orbit sander with 4 6" pads underneath.
Despite the guffaws, you're on the right track. You're using the right sander, especially for a novice!
I wouldn't have started with 24-grit paper, but I know that's what some people suggest for that particular kind of sander.
If I were you I'd move immediately to either 60-grit or 80-grit. Keep the sander moving slowly and methodically. Remember that the coarser grit paper is for getting all the crap off the floor.
Then move up to 120-grit or 150-grit, and finish up with no coarser than 180-grit.
Each successive "step" of sanding will smooth up the wood & make it look better.
If I were you I'd carefully remove the quarter-round on the baseboard. It'll allow you to get closer to the wall.