Vietnam has a quite good transportation system, with a wide road, train and airport network. However, like in other SEA countries travelling in Vietnam is notoriously slow, so the saying less is more still applies in Vietnam.
There are 3 international airports in Vietnam: HCMC, Hanoi and Danang. Phu Quoc was until 2015 an international airport as well, but currently there are no international flights arriving or departing. There a quite a number of national airports throughout Vietnam: Buon Ma Thuot, Ca Mau, Can THo, Chu Lai, Con Dao, Dalat, Dien Bien, Dong Hoi, Hai Phong, Hue, Nha Trang, Phu Quoc, Pleiku, Quy Nhon, Rach Gia, Than Hoa, Tuy Hoa and Vinh. So you can reach most parts of Vietnam by plane. Only the area west and north of Hanoi is airport free.
For domestic flights you can either use the country’s airline Vietnam Airlines (www.vietnamairlines.com) or the low-cost airlines VietJet Air (www.vietjetair.com) or Jetstar Pacific (www.jetstar.com). I flew a few times with Vietnam Airline and VietJet, and all 7 flights were ok, with only one flight with Vietnam Airlines delayed by 2 hours. The reviews of Jetstar is not very good, so I have avoided them so far. However, in general the % of delayed flight is quite high in Vietnam, so it is highly recommended to spend the last night in Vietnam in the place of your flight home. The risk of missing your flight home due to a delayed domestic flight is not worth it and can become very expensive.
Most international airlines fly into HCMC, with the usual stopovers. Vietnam Airlines offer non-stop flights to several European and American airports. Some airlines like Emirates also offer flights to Hanoi as well. So if you plan travelling from north to south Vietnam, it it might be worth to see if you can fly into Hanoi, and leave from HCMC. Several Asian low cost airlines like Nok Air and Air Asia also serve HCMC, Hanoi and Danang.
So far I flew with Air China and Thai Airways to Vietnam, and I was surely impressed with Thai Airways as they offered shorter layovers in Bangkok. Bangkok is in general a great transit airport.
Overall, flying is a good option and affordable method to travel through Vietnam.
If you have a connecting flight straight after arrival in Vietnam to your final destination in Vietnam on a different ticket I would advise having around 3 hours or more between flights as you have to pass immigration, get your bag and checking in again (last check-in 40 minutes before departure). During peak times waiting time at immigration can be longer. If you are flying on one booking I would be less worried, as the airline will just put you onto the next flight.