Here is some info from the BATF site:
"(B8) May a nonlicensee ship a firearm through the U. S. Postal Service? [Back]
A nonlicensee may mail a shotgun or rifle to a resident of his or her own state or to a licensee in any state. Handguns are not mailable. A common or contract carrier must be used to ship a handgun. A nonlicensee may not transfer any firearm to a nonlicensed resident of another state. The Postal Service recommends that longguns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms.
(B9) May a nonlicensee ship a firearm by carrier? [Back]
A nonlicensee may ship a firearm by carrier to a resident of his or her own state or to a licensee in any state. A common or contract carrier must be
used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract
carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm. [18 U. S. C. 922( a)( 2)( A) and 922( e), 27 CFR 178.31]
(B10) May a nonlicensee ship firearms interstate for his or her use in hunting or other lawful activity? [Back]
Yes. A person may ship a firearm to himself or herself in care of another person in the state where he or she intends to hunt or engage in any other lawful activity. The package should be addressed to the owner. Persons other than the owner should not open the package and take possession of the firearm."
here's the source document.
There will probably also be State laws to check at source and destination.