Instructions
Online gun dealers will first need to run a background check on you using the FBI's National Instant Criminal Background Check System (NICS). This is the same as it would be at a local gun shop if you were looking to purchase a firearm. They'll need your personal information to do this so make sure to supply that to them when you are asked. If you are approved you'll be able to purchase right away, but if you are flagged for an actual person to look at your results you may have to wait a week or so.
After you have been approved you'll have to contact a local gun shop that will be able to receive your firearms for you. Online gun dealers aren't allowed to ship guns directly to your house so they will ship them to a gun shop that you choose and you will be able to pick your firearms up there. This is a protective measure to make sure that someone doesn't get a hold of your gun in the mail and that someone other than you doesn't receive it from the mailman.
At this point you should be clear to order from online gun dealers as long as you've properly set up the relay with a local shop. All you have to do is pick out the guns that you want and purchase them. Since it's an online transaction you'll need to use some form of electronic payment such as a credit card. If you have any questions about a particular firearm make sure to call the online gun dealers before you actually buy it because it's a big hassle to ship and return guns.
When your transaction is complete they'll give you a receipt email and a tracking number so you can follow the shipping status of your gun in the mail. When the local shop receives it they'll call you and you'll be able to go pick it up.