how do I share a song in my library with a friend?

First, the friend must be using Apple Music.

Second, you cannot share your entire library with them. What you CAN do is share playlists, individual songs and albums with them.

While viewing a Playlist, Song or Album on an iPhone, tap the "..." information icon. There will be two "Sharing" options.

"Share (Playlist, Song, Album)" OR "SharePlay"

Using the "Share" option allows you to send the item to your friend via iMessage, AirDrop or even Email.

Using the "SharePlay" option allows you to listen to the song/album/playlist at the same time via internet connection.

Hope this helps!