You can select a character you want to add as a friend,

or you can send a request to them by entering their character name in the top right Menu list > Community > Friend Request menu. If it's accepted, the character will be added to your Friends list.

At the bottom of the Community window, you can see your Friends list, as well as a list of your received and sent Friend requests. 

If you're a member of a guild, you can also see a list of all your guild members and who's online in the Guild tab.