Here's a rundown of the process, largely culled from some earlier posts of mine, with some edits.
It's illegal for nonlicensees (you) and 03 FFL C&R licensees to send a handgun via the U.S. mail. Period. It's a violation of postal regulations. You may find some people who claim it's legal because it doesn't show up in the federal firearms regulations, but they're not looking in the right place. Only licensed dealers, manufacturers, and pawnbrokers may mail handguns.
Nonlicensees can send a handgun out-of-state via UPS or FedEx, but company regulations require that you send it next-day air rather than ground. Furthermore, you may NOT ship a gun from a drop box, regular business pickup, or one of their strip-center "UPS Store" locations, which are franchises and aren't authorized to handle firearms. You typically have to ship guns from an actual company-operated hub, although I'm told that "FedEx Office" outlets will now handle firearms. Hubs can generally be found at your nearest commercial airport with scheduled airline service. The inconvenience of reaching a hub or FedEx Office location may be a deal-killer if you live in a rural area.
Generally the cheapest option is UPS "Next Day Air Saver", which doesn't guarantee AM delivery, but will save you $8-$10. However, the package will still typically cost $35-$60 to the CONUS and substantially more to AK or HI.
Federal law requires a FFL transfer on the receiving end. Although it's technically legal, not all FFLs accept shipments from unfamiliar nonlicensees; this is a private business decision to avoid potential legal hassles if the shipper's ID is illegitimate or missing, or the gun turns out to be stolen or illegally modified. ALWAYS check with the destination FFL
before you ship, or they may reject the shipment!
03 C&R FFLs may accept C&R-eligible guns shipped directly from out-of-state nonlicensees, but the gun
must be C&R for the shipment to be legal. Make sure there is no doubt about the gun's provenance before engaging in such a transaction.
Due to the expense and hassle, it's often cheaper and easier to send handguns via a Dealer FFL because they can ship in a USPS Priority Mail Flat Rate Box. Most handguns will easily fit in the "Medium" box and ship for $10.70 anywhere in the USA, including AK and HI- an instant ~$20-$30 savings over the cheapest UPS/FedEx rate.
The difference in cost between this and Next Day Air will probably offset the FFL transfer fee.
Some unethical folks will tell you "well, you can lie about what's in the package and send that handgun by UPS Ground...", but you will lose any hope of recovering any insurance compensation if the gun goes missing. Air shipments are subject to extra security, hence the policy.
By federal law, nobody can require you to label a package saying that it contains a firearm. This applies to the USPS and common carriers equally.