How do you send a dog to another state?

You must register your dog with the appropriate government institution. Most modern countries require medical records and for the pets to have all of the required shots. Some countries now require people who are moving their pets there to implant RFID chips in them, which helps keep diseases like rabies under control. As far as shipping the dog goes, outside of most airports own pet carriage services, there are many businesses who provide pet relocation services.