I've flown with rifles / handgun many times. Minor hassle so allow a few extra minutes at check in. You'll obviously need a good, hard-sided, locking case to protect them and meet TSA requirements. I have a few Pelican cases and the most used is a 1750 if I recall correctly - it has wheels so its a lot easier to handle.. TSA has requirements for the cases but a Pelican or something similar should be good to go.
It has to be locked -
NOT with a TSA lock. Its advisable to not put gun related stickers on it to avoid making it a target for theft, etc - I keep mine blank with the exception of a very small name / address sticker.
When you check in you will have to declare any firearms or ammunution you have as all are subject to inspection to ensure they can be transported safely. Mostly, I'm asked to walk down to an area at the ticket / check-in counter where the gun cases are opened and insepcted to make sure chambers are empty, etc. and then YOU lock it up in front of them with you non-TSA lock and keep the key with you (combination locks are OK too).
A TSA lock is a no-go for gun cases.
Firearms or ammo cannot be in carry-on bags or otherwise carried in the passenger cabin of airlines. (Remote fly-outs may be more flexible)
Ammunition can be in your regular checked luggage and you do not have to go to another area for inspection in most cases. Ammo needs to be in the original box or something similar. Sometimes they want to see it but quite oftern they don't look if I tell them its in the original box.
Relaoding powder / primers may not be transported on airlines.
Be aware of the airlines size / weight limitations as its easy to go overweight with a large Pelican case with a couple of rifles and other items. Depending on the airline it could be cheaper to have 2 cases that meet weight limits than 1 overweight case.
TSA website regarding firearms
The above is related to domestic travel in the US.
