What you are looking for is a connection table connecting users to itself. The entry in this table will represent the friendship between one user and another.
User table
UserID | UserName | FirstName | LastName ...
Friends table
ID | UserID | FriendID
Both UserID and FriendID will be foreign keys in the Users table. You probably want to have a unique constraint for the pair (UserID, FriendID) and a non-unique index for the UserID. Note that UserID is PK for the Users table, and the identifier is PK for the Friends table. Using a separate PK table for friends will make it easier to access a specific user / user pair in your interfaces.
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