I've traveled with my firearms for over 5 years now, and I know the drill pretty well, so here are a few tips I've picked up.

Know the federal regulations. The TSA's website is a good source.

A locked hard sided case is required to transport firearms. No ifs, ands, or buts on that.

Some airlines will not transport firearms, while some will not transport the maximum number you are allowed to. Check the airlines baggage info on their website to make sure your carrier will accept them.

If your weapon is an auto loader, remove the magazine and use a cable lock to enable the screener to quickly verify the weapon is not loaded, and is not currently operable. This is not required, but it helps.

Every airport is different. I have never traveled to one where my rifle case did not come out at the carousel with the other bags. This is why I'm damn sure I get to the belt and position myself to grab the case ASAP before it passes anyone else.