Packing tips: Wrap your bottles in a plastic bag. Wrap everything in a garbage bag. Pack WELL around it all. If it leaks the shipping company will not like it.
The entry forms and bottle ID forms will be downloadable from the website hosting the competition. In general you will fill out an entry form with the name of beer, style etc. Each bottle will have a small label with some information as well, but remember you can ONLY attach the bottle ID tag with a rubber band! The instructions should supply all pertinent information.
Don't ship via US Postal Service. It's against the law.
You can ship via private company, like UPS. It's only against their policy, so you won't get arrested or fined. And don't write "BEER" on the side of the box!
The AHA competition is a HUGE event. I am sure there are a great number of persons from this site entering.