How to fly your pet?
You will need to buy a crate for the dog. The airlines will usually recommend someone for the crate as they have particular standards. Besides that, all you will need is a certificate of good health from your dog's vet and all his/her vaccination certificates up-to-date. The vaccinations have to be done a month prior to the flight date. On the day of the flight, you need to report at the airport 3 hours before the flight timing.
Also, planes have high oxygen pressure about 2 to 3 hours after taking off, only planes with sufficient air pressure would take the pet in their boarding, so you need to check that also before moving for the airport, as the airline will then shift to their next flight.
Inter country dog transfer needs also a blood check in addition to the things mentioned above. The blood sample has to be sent to the other country 3 months before you are scheduled to fly. All the vaccinations should not be more than 3 months old. Your dog should be chipped.
You have to check in your pet 3 hours before departure. Feed him at least an hour before flight. A medical check is done by the flight doctor to be sure your pet is not sick or sedated. Such pets are not allowed onboard.
All I can say is that flying is as safe for your pet as it is for you. Just be careful to choose the right flight (most expensive one) and don't forget to give the company, specific details about your dog for example it is scared of darkness, etc.
Flying into the US, the dog will be quarantined to check if it is carrying any germs and diseases. Even if the dog did a round trip from US to an international destination and back, the dog will be quarantined.
For train journeys applicable only in India
A few months ago, I traveled by train from Delhi to Asansol. Since there are no flights on that route, one has to take a train. I had to take Pooh along with me, and I was quite apprehensive about the train journey with a full-grown lab. But guess what, it turned out to be a great experience. I traveled by Rajdhani Express and it was only an overnight journey. The railways allow you to take your dogs along with you when you are traveling in AC first class, so I got a first class ticket and we had a coup (meaning both the berths were ours), so Pooh was with us in the coup and she loved the journey.
In case, there are no AC first classes, or its something you cannot opt for, you can still take your dogs by train. You will have to put them in the guard coach where a cage is available. This is not a very comfortable arrangement, but for short journeys, this can be availed.