Players can be added to your friend list by clicking the 'Add Friend' button from the Player Info screen:
Clicking this button will send them a friend request, which will then need to be manually approved in order to become friends in-game. You can manage your friend list, as well as any pending requests, from the Social menu, which can be accessed at any time by clicking the following icon:
This panel also allows you to manually search for players by clicking the 'Add Friend' tab, and entering in their player ID number. Please note that only numerical characters are allowed for entry here. To find your player ID number, simply open your in-game profile and it will be displayed just beneath your username.