You can play on multiple devices by linking your game to your Google, Apple, or Amazon account. You are asked to sign in when you start the game. If you skipped this step, go to Game Settings - Community - Sign in

After that, your game progress will be saved on all devices connected to this account. 

Unfortunately, you will not be able to have the same progress on devices with different operating systems, such as an iPhone (IOS) and an Android tablet, as Google Play and AppStore do not share data.