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.