This walkthrough is using an android device, but the steps are similar for the iOS app.
On your mobile device, tap the Play Store (Android) or App Store (iOS) icon to open the app.
In the search bar, type Microsoft Authenticator and tap Microsoft Authenticator.
Tap Install and wait for the app to install.
Be sure to accept or give permissions to use the camera to scan the barcode.
When the app opens you can scan the barcode there and you're good to go.
The video walks through the entire process, but for those who want quick steps the above is all you need to do is just get to the point where you can scan a barcode.