The universal search bar on Snapchat is on the top of the screen. You just tap it to start searching.
When you first tap the bar, results like "new friends" or "frequent chats" (if you have them) show up.
When you start typing, live results start to appear. They can include friends, publishers, chats, and users who you aren't yet friends with so you can add them.
You can swipe right on the search landing page to just get a list of your contacts. In this case, there are no contacts, so we're prompted to find friends.