There are several ways for you to travel with your pets. Some airlines will allow passengers to carry a pet on board such as a small dog or cat if it is in a proper FAA approved carrier. The airlines do limit the number of pets on board, so if you are traveling with a pet the sooner you inform the airline the better your chances to travel with your pet. The airlines will also charge a fee for this service.
If you are traveling with a larger pet some airlines are equipped to have a pet in the cargo bay, otherwise you must ship your pet. Fees will apply for any of these services.
If a passenger is traveling with a service animal, and has proper paperwork when required, there are no fees and most airlines will accept them as long as there is room on the flight.