It is very simple to download music from Youtube, all you need is to find the song you are wanting on youtube and grab the link for that specific video!
Next, you need to find some service that allows you to paste the link there, and it will convert the song for you from a video file into an audio file. There are many websites that will do this for you for free such as the websites below.
Once you have the link to the song on youtube that you want to download, simply copy the link and paste it into the URL box on whichever converter website you choose, and then click convert and download. In the video below I show you how to do this.