What do service members need to privately transfer firearms?

Yours is a VERY broad question. In the US, a service member stationed in a state other than his home is considered a resident of the state where he is stationed for the purpose of acquiring a firearm. When purchasing a firearm, he will need to comply with state and local laws at his location. He will need a copy of his orders assigning him to that state, as well as 2 IDs that show his name and address.
Yours is a VERY broad question. In the US, a service member stationed in a state other than his home is considered a resident of the state where he is stationed for the purpose of acquiring a firearm. When purchasing a firearm, he will need to comply with state and local laws at his location. He will need a copy of his orders assigning him to that state, as well as 2 IDs that show his name and address.