What size is the dog? Small enough to go as carryon? If so I like that option the best.
If not cargo isn't horrible. I have shipped many times to and from. I like most airlines, but they all have had a few bad times so you just have to be as careful as possible and read, read, read.
Most of the time you don't need a health certification flying as carryon in the states (Hawaii is an exception - no carry on to HI and dogs have to be quarantined.) if the dog isn't going to stay in the state it is going too, but you need to check with the arriving states rules as states set their own (department of agriculture generally handles this).
If the dog is to fly cargo a health certificate always needed and generally it must be within 10 days of the date of travel. They must be current on Rabies shots as well, and must be in good health. I recommend that you have Rabies, DHPP, Bordetella, and de-worming all current before the pet flies.
I also DO NOT believe in sedating them most of the problems that I have heard of have happened because a dog was sedated.
If you are doing cargo...here is a couple of pointers....Put in something that smells like you in the crate...I pair of worn socks or something, freeze the water bowl you are going to attach inside the crate, this will thaw slowly and give the pup water throughout most of the trip. Put a food in a dish attached inside the crate too. I also tape a small bad of food to the top of the crate along with any papers that need to go with them to insure they are as safe as possible. I include a sheet with all my contact information on it and an alter contact from both origination and destination locations. Better to be safe then sorry.
Most airlines also have heat and cold cargo restrictions so you have to be aware of that as well. As a general guide over 80F no cargo...under 32 no cargo. Some airports also have their own rules on heat and cold and block either by temp or dates.
If you are going overseas the rules multiple even more and you maybe required to have a USDA certified health certificate. Which can be done in Annapolis, MD if required. They aren't easy to find, but they will help you get to the office. Also each country has it's own set of rules and all kinds of requirements from ISO microchips, flea and tick treatment, titers, and specialty shots are all possible requirements, as well as quarantine. Each country sets their rules and most of the time you can get this information from the countries embassy.
Bottom line ask your vet, ask the airline and ask the state you are traveling too all the questions you can think of. If you need help you can PM me and I maybe able to find a link online for you to get more information.