Airline Regulations
Not every airline accepts pets for travel either in cargo or in the passenger cabin, and those that do have their own specific rules, so you'll need to check your airline's website. A specially sized, labeled and outfitted kennel/carrier will be required as will a vet's health certificate issued no earlier than 10 days before you travel.
In the Cabin
Each airline allows per flight a certain number of small pets that can fit in carriers under their owners' seats. Your cat must remain inside the carrier throughout the flight, so it's a good idea to book direct, nonstop flights. Fewer airlines are dealing with individuals, preferring to deal with customer-hired pet transport companies that are licensed to take care of the details, including adhering to federal and health requirements.
Checked Luggage
You can have your cat travel as checked baggage, which means he will fly in the cargo hold alongside the plane's luggage. The cargo hold will be properly ventilated and pressurized.
Considerations
Obviously, it's neither simple nor inexpensive to travel with your cat. However, you can't put a price tag on the safety and well-being of your animal. You'll pay the airlines (in addition to standard fees, you may have to buy their regulation carrier), you'll pay the vet for the special exam, and you'll possibly a pet transport company to work through all the red tape for you.
Warnings
Even after all the time, effort and expense, the airlines have the right to refuse to transport your cat on the day of travel. They can cite a variety of reasons, from excessive heat or cold in departure or arrival cities to poor kenneling to pet odor or illness. Vets have issued an important health warning, too: don't sedate your pet since sedatives and high altitude can interact negatively.