How can I connect to other people's games in local multiplayer?

You must be on the same WiFi network, and the device with the world must be playing in the world. As soon as the host leaves, everyone gets kicked out.

This is how I solved the problem:

For a home LAN MineCraftPE server, I simply:

• Used an old iPod Touch (Gen3 or newer),
• Installed the app (free since I already bought it),
• Set lock screen time to "never" (Settings > General > Auto-Lock > Never),
• Start the app
• Set volume to zero
• Place on shelf on charger

• Forget

  This gives me a free, full feature, no maintenance Minecraft server. The world is always available. You can copy an existing world from your current device with free programs like iExplorer.