A friend just invited me to join him when he goes deer hunting in Colorado this fall. Do I ask Delta Airlines to transport my weapon, or do I have Fedex mail the weapon to the hotel I will be staying at? What is the standard operating procedure for someone to take their weapon with them hunting in another state where they have to use an airline to get there?

You can transport your firearm through the airlines. Just make sure it is in a hardsided case and unloaded. The case will need to have locks. You will need to declare it at check-in and go to the tsa counter for them to check it in. Ammo must be in it's original box. Not a problem at all.

has to be unloaded of course.

I really like the pelican rifle cases.

don't you have to ship from a FFL to another FFL? if not how much does it cost to ship via fed ex etc...?

Taking your weapon with you when you fly is really no big deal, I used to do it all the time. Now I just bow hunt and I take that with me as well, but I drive now to were Im going as I just hunt in the midwest.