You can save a video by clicking "Save This" on the player page. You can save playlists or networks to your Favorites using the "Add to Favorites" button. To view your Favorites page, click on "My Video" in the header to go to your profile page where all of your Favorites are displayed.

All Favorites are public by default, but if you want to make them private, click the "Edit Profile" link from your profile page and change the setting for your Favorites to "Just Me". If you choose to make your Favorites private, your videos, playlists, and networks will all be private and visible only to you. You can also remove anything you’ve favorited by clicking on the "Remove" link.