Games are more fun with friends! Go to the friend menu in the in-game lobby for all the friend options.
Enter your friend's display name and click 'Add Friend'. Once they accept your friend request, they'll add to your friend list. Easy peasy!
If you're playing a Squad mode, you can also create a party so you can group with your friends for matches. (Or, if you're feeling adventurous, you can skip the party and group up with strangers!)
If someone invites you to their party, this is where their invite will be waiting for you. Accept the invitation to join a party!
You can set your status to online, invisible, or away. This is the status that will show on your friends' lists for your name.