You need to do it in two separate stages. Firstly you need to save the Youtube video to your computer and then you need to burn a DVD.
There are countless websites, programs and browser extensions which claim to help you to be able to accomplish the first part of your task. A problem with all of them though is that Google (who own Youtube) keep finding ways to render them useless. (Google pays fees to TV and film companies to allow clips from their output to be streamed on Youtube but it's technically illegal to save such content to your hard drive, as no licence fee has been paid to do so). So many of the ways of saving Youtube videos to your hard drive can be unreliable. (i.e. they'll cease working for a while until their developers find a new way to outwit Google in the constant cat-&-mouse game which they play).
The method I use though is to view Youtube output in Firefox with the Easy Youtube Video Downloader Express extension installed:
https://addons.mozilla.org/en-GB/firefox/addon/easy-youtube-video-download/
It adds a 'Download As' button to Youtube pages viewed in Firefox. Clicking on that button allows you to choose whether you just want the audio (MP3) or which video format you prefer. (Select MP4 for your needs). It also allows you to select your preferred video resolution (360p, 720p HD or 1080p full HD) subject to two caveats:
(i) you obviously can't download a video at, say, 720p if it was only recorded at 360p in the first place ; and
(ii) to be able to download at 1080p you need to make a donation for the 'PRO' version via PayPal. You can choose the amount you donate though, from US$30 down to US$5, depending upon what you think the service is worth:
https://videodroid.org/pro_upgrade.html
Once you've selected your preferred format you'll then be able to choose where to store your video (in the same way that you can choose where to save Word documents or images on your computer).
As I've already indicated, there are many, many other ways of saving Youtube videos to your hard drive but many of them only save at 360p and some of them only save in Flash video (FLV) format, which you'd then need to convert before burning your DVD. (To the best of my knowledge, Easy Youtube Video Downloader Express is currently the
only way to save at 1080p).
Once you've downloaded your videos to your hard drive you'll need to burn them to a DVD. (I'm assuming that your computer comes with a DVD writer or re-writer, and not just a drive which can only read DVDs!). Note that there are two ways of doing so. You can either burn them directly as MP4 files (to a 'data disc'), meaning that you'll only be able to use the DVD in your computer, or you can burn them to a DVD which can be used in most DVD players. (That option will be called a 'video disc', or something similar, in your burning software).
The disc burning software incorporated into recent versions of Windows can probably do the job but this freebie is far better:
https://www.ashampoo.com/en/usd/pin/7110/burning-software/burning-studio-free