Quick answer: Tap Save under the video and choose Watch later. Find the list in the You tab. For videos you'll need again, like tutorials or recipes, save the link somewhere searchable instead, so it doesn't get lost in the Watch Later pile.
You find a great video at the wrong moment: on the bus, in a queue, two minutes before you have to go. Saving it takes one tap. Finding it again a week later is the part that usually fails.
Option 1: Watch Later
Under the video, tap Save, then choose Watch later. You can also do it from a feed: tap the three-dot menu next to any video and pick Save to Watch later. Your list lives in the You tab, under Watch later.
Watch Later is perfect for entertainment you plan to watch this week. It's bad for anything else, because it's one long list ordered by when you saved things, with no notes and no way to tell which video was "the one about fixing the sink."
Option 2: Playlists by topic
Tap Save, then New playlist instead of Watch later. Make a playlist per purpose: "Workouts," "Recipes to try," "Guitar lessons." Keep it private unless you want to share it. Playlists beat Watch Later for anything you'll come back to more than once, as long as you stick to a handful of them.
Option 3: Save the link outside YouTube
Some videos aren't really "videos to watch." They're reference material: a tutorial you'll need the next time something breaks, a recipe, a talk you want to quote. Those belong next to the rest of what you've saved, not buried in an app you open to be entertained.
Tap Share under the video and send the link where you keep things. In Snugit, that's one tap from the share sheet, and the video's title comes along with it, so searching "sink" or "sourdough" finds it next month. If a specific moment matters, add a quick note with the timestamp ("fix starts at 4:30").
What about downloading?
Downloading for offline viewing is a YouTube Premium feature, and the downloads live inside the YouTube app. That's handy before a flight, but it's not a filing system. For anything you want to find again, the saved link is what lasts.
A simple rule
If you'll watch it for fun this week, use Watch Later. If you'll need it again, save the link where you can search it. That split alone stops Watch Later turning into a list of 300 videos you'll never open, which is the real reason most saved things are never seen again.
Get Snugit and save the videos you'll need again, right next to your links, notes and files.