Make sure you have activated the Friend feature, in the Configure Site > Social Networking page. You will want to jump to the "Friend" section, either from the Configure Site > Social Networking drop down menu, or the top "Friend" link on the Social Networking page.

 

If you are using the default Public Profile page, the add friend button will display on another person's profile. Otherwise, you just add the Placeholder Text to it on your Public Profile page: