Step 1. use
free youtube downloader for Mac to download youtube videos to mac
"iSkysoft free Video Downloader for Mac is a totally free video downloader for downloading FLV videos from YouTube, Yahoo, Google, Break, Metacafe, MySpace, Gofish and other video sharing sites. It automatically detects the internet videos and allows you to download full-length movies played in Safari and Firefox browsers on Mac OS instantly."
Step 2, Then you can use freeware
burn to baccup youtube videos to DVD.