There are six ways to add friends:
1) Add friends using a player ID.
For details, see How do I add a friend using a player ID? in this FAQ.
2) Send a friend request to a visiting player.
For details, see Can I become friends with visiting players? in this FAQ.
3) Send a friend request to other players who have visited your campsite or helped out in your garden.
For details, see Can I become friends with other players who have visited my campsite or helped out in my garden? in this FAQ.
4) Find and add friends from other apps linked to your Nintendo Account.
For details, see How do I become friends with friends from other apps I have linked to my Nintendo Account? in this FAQ.
5) Add friends by sending an invitation via e-mail or text message.
For details, see How do I add a friend by sending an invitation via e-mail or text message? in this FAQ.
6) Add a friend in person using sound.
For details, see How do I add a friend in person using the Send a Tune feature? in this FAQ.
* From Version 5.3.2 and on, you will no longer be able to search for friends via Twitter.
However, friends you have added via this method will still remain on your friends list. They will not be removed.