A full wing has 4 players total so you will either need 3 friends to join you, or find some random people online or on the site here to join up.
You'll all have to be in the same system and close enough together so you can see each other's names in your close contacts. Once you are close enough hold 'X' and press up on the Dpad to bring up your Comms. From here select the pilot you want to add to your wing and it should have the option to invite them. Form a full wing of 4 players and the achievement will pop for everybody, not just the person who sends the invites!
One other thing to note is the wing only lasts until you quit the game; every time you restart the game you'll have to all meet up to form it again.
-edit-
Looks like I was mistaken about having to be in the same system, or else they've changed it so you don't have to all be in the same system anymore, cheers!