How to become friends to an existing user?

Click on "Find Friends" tab on Left Sidebar. Enter name of the friend in the search bar and click "Search". If you find the person you are looking for in the results click on his name. You will be taken to his profile page. Scroll down to the "Relationships". There you will find the link "Become xxx's friend". Click on that and write elaboration, if required, and click send. Once your friend approves your request you will become friends with him.