In order to get a gun in the U.S., you have to go through the infamous Brady background check. The check works differently in different states, but in Colorado, in involves filling out the ATF gun transfer form, showing the dealer some valid ID, then the dealer calls the Colorado Bureau of Investigation's background check service and gives them what you filled out on the form. The check usually doesn't take more than fifteen minutes, assuming they aren't too busy and there are no complications.
Some of the less gun-friendly states add hassles to the procedure. California has a mandatory waiting period, Virginia has the one-gun-a-month law, Chicago requires a permit from the police to get a handgun (strangely enough, the forms to apply for the permit are unavailable.)
It doesn't appear that Louisiana has any truly obnoxious gun laws - no permit required for anything that isn't Class III, "shall issue" CCW, a bunch of hunting regulations. You should be able to get a gun in 15 minutes.