Hi Ivan,
Just click on someone's name and then from the 'actions' list on the right hand side of the screen select "Add to my friend's list". You can then write a hello greeting in the text box provided (or just use the standard greeting that is suggested) and click the submit button.
The person will get you message and if they agree to be your "friend" on chess.com then they appear in your "friends" list.
hi to every one, i am new member of this site, i dont have a time to explore this sites, i want to have friends with this site, how can i add a friend.. thanks..