How do I make a playlist on YouTube, and can I keep it private so only I see it?

Two ways to create one. From a video: click 'Save' (the bookmark icon) under it > '+ New playlist', name it and set the privacy. Or go to the left menu > 'You' > Playlists > New playlist. When you make it, pick the visibility: Public (anyone), Unlisted (only people with the link), or Private (just you). You can change that later in the playlist settings. To add more videos, hit Save on any video and tick the playlist, or use the playlist's own 'Add videos' search. On mobile it's the same Save button under each video. Reorder by dragging in the edit view.

Set it to Private if it's just for you, or Unlisted if you want to share the link without it showing on your channel. You can flip that setting anytime in the playlist options.

The 'Save' button under any video is the fastest way in, it lets you tick existing playlists or spin up a new one on the spot without leaving the video you're watching.