There are several ways you can find and add new friends in the game:

-If you know their Nanobit ID, you can just send friend invites from the Friends tab in the Social menu.
-You can also add other people if you switch from the Friends tab to the Others tab. You can visit them and then add them as friends.
-Similarly, if you tap on your status in the top right corner, and switch to one of the leaderboards, you can visit and add the people there.