Once you're on a person's page, you will see the grey bar has changed to show you the categories of information about that person. Instead of "Your Profile", "Your Friends", and "Your Movies", you will see links to those sections for the person whose page you are visiting.
If the person is not already your friend, you can add them from their homepage. You will see a button under their profile that you can click to add them as a friend.
Clicking that button will display an option for you to choose how much you trust this person about their movie choices. Think of this as if the person were to have rented a movie to watch, how likely is it that you would want to see that film. This rating is given on a scale from 1 - 10. A rating of 1 would mean you don't trust them very much, and a rating of 10 means you trust them highly. Once you select a rating and click "Add" the person will be added to your friends list. You will have the opportunity to change the rating at any time. This trust rating is totally private and your friends will NEVER be shown the trust rating you gave them. It is important that you are honest with this rating because it will affect how well the system can personalize the information it shows you.
If you add a person as a friend, you will show up on their friends list as someone who has added them as a friend. The person will not necessarily make you a friend back.
Once you have made a person a friend, you will see their trust rating under their profile. There will also be buttons that give you the option to change your rating for the friend or remove them from your friends list.