
In what respect as clearly the only places to travel a dog, without flying, from the States, would be neighbouring countries. Otherwise it's flying!! And if coming to the UK, you'll have to comply with the DEFRA Pet Passport regulations, which currently are easier than they used to be (if not better in terms of protection the UK from infection coming in).
For the actual flight, you should contact the airline you prefer (I tended to use the airline of destination which seemed to mean clearing through was faster .... in other words going to Canada from the UK, we used Air Canada, and coming back, British Airways). That may have been my imagination however.
You'll need to get your dog well used to being crated, if he isn't. Buy an airline crate and set it up with the door open so your dog starts to being used to being in there. Don't plan on using sedation - most airlines don't like to take sedated dogs in any case, and if it's a long flight, it's far better the dog doesn't come round mid-flight, and panic. I didn't sedate mine.
If you are looking to import, for specific bloodlines, I'd do your homework. And it might help to talk to people in your breed, to see how they feel/what they know, about the various overseas lines, so you don't waste your money. I have imported, but always look at the bloodlines first - any possibility to show is an added bonus. To me.