How does one add boarding passes to Apple Wallet?
If your airline is Delta

Check into your flight with this page of Delta's website on your iPhone/iPod Touch (have your flight's confirmation number ready). When you complete your checkin, you will be given an option to add the pass to your Passbook (aka Wallet app). Tap into that, then press the Add button to add the pass to your wallet. Then you can skip the check-in kiosk at the airport if you have your phone and the pass handy.



Any other airline

Download the airline's app (yep, only Delta lets you use the mobile site to add a boarding pass to Wallet) and open it up. Here are some apps from the major carriers (though don't fret if your airline is not on this list, it's rather incomplete; just search for it in the app store):


United
JetBlue
Alaska
American Airlines
RyanAir


Proceed into the app (have your confirmation number or loyalty account info ready) and choose the Check in option (location of this button varies between apps). Follow the instructions to check in, and at the end, you'll see a button to Add to Passbook or Add to Apple Wallet. Press that, then press the Add button in the Navbar and you'll be set.