New [Fall 2023): Free Music Archive now requires an free account to download music. If you don't want to make an account, check out Incompetech; music can be downloaded there without an account.
While it is against Youtube's terms to download videos that are not your own, there are many Creative Commons videos on Youtube which are legally allowed to be reused according to their license terms.
There are many tools for downloading Youtube videos and they frequently change. Explore these articles to find the latest working tools and more information on the issue.
If you are using Garageband, you must import and export the YouTube video into Audacity first. You can import the video by dragging it into Audacity and then you can export it as an MP3 file, which you can then load in Garageband. Importing an MP4 video file directly into Garageband will include the video file and may cause issues with your project.