This article explains the two methods to create a private story in the Snapchat app. Instructions apply to recent versions of the Snapchat app for iOS or Android.
How to Create a Private Story on Snapchat
The Snap tab refers to the area of the app where your device’s camera is activated, allowing you to take a photo or record a video. To find it, tap the circle in the center at the bottom of a tab, or swipe left or right from the Conversations tab or Discover tab.
Take a photo or record a video in the Snap tab.
Tap Send To at the bottom right.