Using Instagram's built-in features:

Save Video: This is the easiest and safest option for public videos. Open the video, tap the three dots in the top right corner, and select "Save Video." The video will be saved to your camera roll (Android) or camera roll/Photos app (iOS).
Limitations:

Only works for public videos.
Doesn't offer different quality options.
Using third-party websites:

Online downloaders: Websites like SaveFrom, InstaDownloader, and iGram allow you to download videos by pasting the video URL. They offer more features like choosing quality and format. https://saveinsta.cam/