You can add a user to your contacts list by clicking on the "Add to contacts" link on video player pages or on a user profile page. You can choose to categorize them as "Family" or "Friends", or simply just add them as a contact. You can also make your contact private by unchecking the box that says "Let others see (username) in your contacts" under "Display Options". Then when you are signed into Yahoo!, you will see the status of your relationship with them on their profile page (example: "In Contacts").
If you want to change the status of your relationship or delete a contact, click on the "change" link next to the relationship status and you will be able to change the category or remove them from your contact list.