YouTube Audio Library Tutorial
Visit your user icon in the top-right corner of your screen. Once you do this, you will get a drop-down menu that will look one of two ways (see below). CLICK "Creator Studio".
Find the video you want to add music to and CLICK "Edit".
CLICK "Audio" - located at the top of your screen.
Now, you should see a menu on the right side of your video containing a list of songs. At the bottom of this menu is a search field. Type in the name of the song you're searching for. There are other search methods, but I've found that if you don't know which song you'd like and you want to sort through them all, you can visit the Audio Library directly.
The song you've searched for should appear at the bottom. Select this song and it should automatically be applied to the video. If you like it, save changes.
Here's a tip!
You can always "Revert to original" if you decide you don't like the song.