Open the YouTube app on your phone
Find the video you want to save
Tap the Download button below the video
Choose the video quality if prompted
Wait for the download to finish
Open the Library or Downloads section in the YouTube app to watch it offline
If the Download button is not available, check whether the video supports offline downloads
If you want to save the video file directly to your phone, use YouTube Premium where available
If the video is your own, use YouTube Studio or Google Takeout to download it