The transfer request requirements and application process are already explained in great detail here and here, so I won't go over those again. The key points are that you need to have a lvl100 toon on retail, and it can't be a DK. You don't need to have an active subscription - you can log into the battle.net website and the game itself in "starter mode" to get to the character selection screen even if your retail account is inactive, and take the required screenshots.
If you want a faction/race change, you need to specify this in your submission. Read the guide I linked above for specifics. If your race/class/faction combo isn't valid for vanilla, you will automatically be given the option to select a new combo on first login. The only thing you can't change is your class - unless you're a monk, in which case you have to change it. In this case, specify your desired class in your transfer application per the guides linked above.
After you hit the submit button, there will be a green notification at the top right portion of the page that says "Your request has been submitted" or something of that nature. There is no other notification, and there's no place to check on the progress. The review process can take anywhere from a few minutes to a couple days, depending on how backed up they are. If you don't get a response after 4 days, try submitting it again. Sometimes the transfer requests get lost in the shuffle (mine did).
When your request is reviewed and either approved or denied, you will get a PM on the forum notifying you of the decision. If it's denied, hopefully they provide a reason and you can resubmit an application with the necessary changes. If it's approved, you can log into the game with your cookie-cutter lvl60 toon.
Your transferred toon will have a randomly-generated name and appearance. There will be a button next to it on the character select screen that will allow you to change these features before you log in for the first time.
Your fresh 60 will be in its race's starting zone. Here's what it will have:
- The blue PvP set for your class/faction (with 0 durability)
Equivelent (ilvl63) PvP belt, neck, rings, and weapon
4 runecloth (14 slot) bags
All weapon proficiencies available to your class maxed at 300
I think that covers all the details. While you are getting a "free 60", you still have a lot of work to do just to get up to speed. Simply buying all your class abilities from the trainer will eat about half of the 500G you start with, and running all around the world on a lvl40 mount to get FPs will keep you busy for a while. The blue PvP gear is sufficient to start running 5-man dungeons, but you'll need to do plenty of gearing up to get into a raid group.