First, open the Snapchat app and tap on a friend's profile. If you have multiple friends with the same name, you'll need to scroll down to find the one you're looking for.
Once you've found your friend's profile, long-press on their name and select Settings from the pop-up menu that appears.
Scroll down and tap Remove Friend. If the person you want to remove is not currently online, they will be prompted to log in before they can be deleted. Once they have logged in, they will be removed from your list.