You can call Delta Pets 1-888-736-3738. They are more than happy to answer questions.
The crate has to be an airline approved, which most crates say that on the label. Crate has to be certain size for the dog to be comfortable, but not big enough to stir up a ruckus!
The top has to be solid and the door must be metal. A food and water dish must be securely attached inside. They want an asorbent material for bedding, no toys (they say). A little bag of food must be attached to the top of the crate. Live animal stickers all sides of the crate. A shipping label with last feeding and age of the animal and much more info is usually provided and you fill out. Phone numbers of you and the new family.
I would say get a non-stop flight leaving early morning if possible.
Health certificate from your vet no more than 10 days old. Rabies certificate if puppy is over 12 weeks.
I would not recommend sending the registration papers with the puppy on the airline.
Call for registration a few days ahead and the weather is a HUGE factor. Too cold, they don't go. Too hot, they don't go.
I have probably left out a few things, but hope I have helped.