There are multiple ways to add friends in Core whether they are strangers or friends by sending them a friend request. Adding friends is a great way to keep track of who is online and manage parties easier.
You can add a player as a friend if you know their username by searching for them using the Add Friend button in the right column of the main menu. You will first need to know their name in game to add them though. This will bring up their name in the search results and you simply need to press the + button.
For adding strangers as friends, you can walk up to them in-game or in the Core World and press F to inspect them. This will bring up several options, one of which is Add Friend. You also open the main menu and on the right is a list of players in game. You can either click the + button next to their name or click their name and then Add Friend. You can also use the Add Friend button to pull up a list of recently played players and send a friend request that way as well.
Once added as a friend, they will show up under the Your Friends category along with their online status. If someone has sent you a friend request, that will show up above the Players In-Game with their name. Playing with friends is easy and can be done either by creating a party or inviting them to your game.
For more information on gaming, check out How to add friends in Pokémon Unite and How to play co-op with Friends in Tribes of Midgard on Pro Game Guides.