Summarize this article:

For devices that run on the Android operating system, look for the icon with the multi-colored sideways triangle (play button). Tap the icon to open the Play Store From the main Play Store page, tap the top left menu button (the three horizontal bars) and select My Apps. Pocket Edition. Scroll through your apps. When you find Minecraft: Pocket Edition, there will be an green Update button beside the app (next to the Uninstall button) if there’s an update available. If there is no Update button, then you already have the latest version. If there is an update available, select Update and it will proceed automatically.  Opt for automatic updates for this app by tapping the three vertical dots on the upper right corner of the app page and checking Auto-Update.  To set up automatic updates for all your apps, tap the top left menu button in the Play Store > Settings, and under General, select Auto-Update Apps or Auto-Update Apps Over Wi-Fi Only to conserve cellular data.

Summary:
Open the Google Play Store. Go to My Apps. Locate Minecraft: Tap update.