When you get to the Grand Floridian security gate, tell the guard you are checking in. He/she will tell you you can pull up for valet parking or unloading or go over to the self park. At this point, do NOT go immediately to the self park area! You'll be lugging all your bags quite a ways. Drive up to the lobby area. There will be bell people there to help unload your car of your luggage. You can then valet park if you want or go over to the self park. If you aren't going to move your car the entire time, I'd use the self park even though it's a bit of a walk. It's not on the other side of the moon but it would be a ways if you had to do it every day.
Then check in, send for your bags that are with bell services, and you are done. If your room isn't ready yet, bell services will store your luggage for you until you are in your room.
BTW - since you are driving, remember that you will have to go through the Magic Kingdom parking lot gates. No big deal, just move all the way over to the right as you can, tell the attendant there that you are checking into the Grand Floridian and you will not have to pay the $11.
It also is a good idea to have your confirmation letter and your photo ID out in case either guard asks to see it or them. I just mention that because my husband always has his wallet in his back pocket and it's quite funny to see him try and get out his driver's license!