They would normally travel in the cargo area - the hold - of a passenger plane. It could be the same plane that you are flying on, or the dogs could fly before or after you, depending what arrangements you could make for someone to look after them.
Contact the airlines you would probably be flying with. Major airlines are very accustomed to flying animals in the hold, and have a special area for them that is pressurized and heated.
The main point is that you MUST get all the paperwork in order as soon as you possibly can. A major removals company like FedEx will be able to tell you what you need to do, and so should the airline.
Do EXACTLY whatever they tell you. Don't take ANYTHING for granted. If they tell you to buy a crate of [whatever] dimensions, DON'T think, 'Oh, the one I've already got that's a tiny bit smaller will be fine,surely'.
I don't think there's quarantine in the US for dogs flying from the UK as long as the dogs have their 'Pet Passports' fully up to date. If they DON'T already have them, be aware it can take six months to acquire one, as the animal has to be first microchipped and vaccinated, then blood-tested six months later.
Contact two or three major airlines right now. Transporting animals internationally is not ever going to be cheap.