Here is exactly what the ATF 'Federal Firearms Regulations Reference Guide' (ATF P 5300.4) says:
(B8) May a nonlicensee ship a firearm by common or contract carrier?
A nonlicensee may ship a firearm by a common or contract 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), 922(a) (3), 922(a)(5) and 922(e), 27 CFR 478.31 and 478.30]

(B7) May a nonlicensee ship a firearm through the U.S. Postal Service?[
A nonlicensee may not transfer a firearm to a non-licensed resident of another State. A nonlicensee may mail a shotgun or rifle to a resident of his or her own State or to a licensee in any State. The Postal Service recommends that long guns 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. Handguns are not mailable. A common or contract carrier must be used to ship a handgun.

[18 U.S.C. 1715, 922(a)(3), 922(a)(5) and 922 (a)(2)(A)]

'Antique' firearms need not be shipped to a licensed dealer. These can be shipped directly to the buyer. An antique firearm is a firearm built in or before 1898, or a replica thereof. The exact ATF definition of an antique firearm is:
Antique firearm. (a) Any firearm (including any firearm with a matchlock, flintlock, percussion cap, or similar type of ignition system) manufactured in or before 1898; and (b) any replica of any firearm described in paragraph (a) of this definition if such replica (1) is not designed or redesigned for using rimfire or conventional centerfire fixed ammunition, or (2) uses rimfire or conventional centerfire fixed ammunition which is no longer manufactured in the United States and which is not readily available in the ordinary channels of commercial trade.

Knives, air guns, accessories, and most gun parts need not be shipped to an FFL holder. We say most gun parts because each firearm contains at least one part that the ATF considers a firearm. This part is typically the part that contains the serial number. This part must be treated as a complete firearm when shipping the item.

Ammunition must be clearly identified as 'Small Arms Ammunition' on the outside of the box. Some shippers treat ammunition as dangerous or hazardous materials.

The section of the US Code that governs modern firearms is called Commerce in Firearms and Ammunition (CFA). This code is available online at: http://www.atf.gov/pub/fire-explo_pub/2005/p53004/index.htm

When in doubt, we suggest arranging for transfer through a licensed dealer. Violation of the CFA is a felony and penalties for violation of it are severe.

The most important thing to know is that you must only ship guns to a licensee. If the buyer is not a licensed dealer, he will have to make arrangements with a dealer in his state to ship the item to.

Before you ship a gun, the buyer must fax or mail you a copy of the licensee's signed FFL license. You can only ship the gun to the address on the license. You must inform the carrier that the package contains a firearm. Of course, the firearm cannot be shipped loaded; ammunition may not be shipped in the same box. You should take the copy of the signed FFL with you when you take the item to be shipped in case the shipper wishes to see it.

Notes on specific shippers:

US Mail: An unlicensed person can ship a rifle or shotgun by US Mail. Unlicensed persons cannot ship a handgun by US Mail. Postal regulations allow the Post Office to open your package for inspection. Ammunition cannot be shipped by US Mail. You can search the US Post Offer Postal Explorer site for specific USPS regulations regarding firearms and ammunition.

FedEx: FedEx will only ship firearms via their Priority Overnight service. Ammunition must be shipped as dangerous goods.

UPS: UPS will accept handgun shipments by Next Day Air only. Rifles and shotguns can be shipped by UPS ground service. UPS will accept shipments of ammunition. Most other shippers will no longer accept firearm shipments. Airborne and Roadway have specifically prohibited firearm shipments.

Since licensed persons are responsible for knowing the law, we are going to assume that you already understand the CGA and know the applicable Federal, state, and local laws.

Notes on specific shippers:

US Mail: Licensed manufacturers, dealers, or importers may ship a rifle, shotguns, or handguns by US Mail. In fact, we suggest that you use the USPS as it is now the most cost-effective way to ship a handgun. To ship a rifle or shotgun, you need only inform the Post Office that the package contains a firearm. A licensed manufacturer, dealer, or importer can ship a handgun</> via the US Post Office if the licensed dealer fills out a US Post Office Form PS 1508 and files it with the local Post Office branch where the handgun is to be shipped. You can search the US Post Offer Postal Explorer site for specific USPS regulations regarding firearms and ammunition.

FedEx: FedEx will only ship firearms via their Priority Overnight service. Ammunition must be shipped as dangerous goods. NSSF members can sign up for a discount of up to 26% on FedEx shipments.

UPS: UPS will accept handgun shipments by Next Day Air only. Rifles and shotguns can be shipped by UPS ground service. UPS will accept shipments of ammunition.

Most other shippers will no longer accept firearm shipments. Airborne and Roadway have specifically prohibited firearm shipments.

The following info comes from the USPS Regulation DMM Issue 54, January 10, 1999, section C-024

Page C-39, section 3.0, Rifles and Shotguns: "Although unloaded rifles and shotguns not precluded by 1.1e and 1.2 are mailable, mailers must comply with the Gun Control Act or 1968, Public Law 90-618, 18 USC 921, et seq., and the rules and regulations promulgated thereunder, 27 CFR 178, as well as state and local laws. The mailer may be required by the USPS to establish, by opening the parcel or by written certification, that the gun is unloaded and not precluded by 1.1e."

Page C-39, section 6.0, PROHIBITED PARCEL MARKING: "For any parcel containing a firearm or a ballistic or switchblade knife, any marking that indicates the contents is not permitted on the outside wrapper or container."

The following pertains only to licensed dealers shipping handguns:

Page C-37, section 1.3, Authorized Persons: "Subject to 1.4, handguns may be mailed by a licensed manufacturer of firearms, a licensed dealer of firearms, or an authorized agent of the federal government......."

Page C-38, section 1.5, Manufacturers and Dealers: "Handguns may also be mailed between licensed manufacturers of firearms and licensed dealers of firearms in customary trade shipments, or for repairing or replacing parts."

Page C-38, section 1.6, Certificate of Manufacturers and Dealers: "A licensed manufacturer or dealer need not file the affidavit under 1.4, but must file with the postmaster a statement on Form 1508 signed by the mailer that he or she is a licensed manufacturer or dealer of firearms, that the parcels containing handguns (or major components thereof) are customary trade shipments or contain such articles for repairing or replacing parts, and that to the best of his or her knowledge or belief the addressees are licensed manufacturers or dealers of firearms."