How is pricing done for delivery across the country?
You will need to shop around. Prices can vary. The dealer may be able to suggest a shipper and possible pay part of it. Usually it is up to the buyer to select a company and pay.
Carvana and other similar sellers will ship but shipping across the country will likely eat up any savings you might get on the car price.
I had a vehicle shipped once and it was about a dollar a mile