There are other ways to lock an iPad in kiosk mode (via an MDM for example) but in this post we will focus on the Apple built-in feature: Guided-Access.

Follow this path to enable Guided-Access:
iOS 13: Settings -> Accessibility -> Guided Access
iOS 12: Settings -> General -> Accessibility -> Guided Access

Set it to ON

Open the App that you want to lock in Kiosk Mode, and triple-click on the home button (the top button on iOS devices without a home button) to enable Guided Access.

Note that there are multiple options you can allow or disable while the iPad is in Guided Access. Make sure you choose the options that best fit your need.

For reference here are some screenshots of where the option is located on both iOS 13 and iOS 12: