Type the first name and last name or his/her email into the search field, press "Enter" or search icon and you will see search results.
Press "Add Friend" to add it to your Friends List.
There might also be your friends who want to contact you through Facebook. Friends Requests you will find on the top menu line of Facebook, check Friends icon (if it is white, it seems somebody wants to connect you).
Other search options
You might also search for pages, groups, photos, videos, public posts