When you buy an app on Google Play, the app is connected to your Google Account. This means you can reinstall the app on your device or install it on your other Android devices without paying for it again, provided that you are signed in to Google Play with the same Google Account you used to buy the app originally. Please see here for more information: https://support.google.com/googleplay/answer/113410
If you are having trouble restoring a past purchase, please contact Google Play support for assistance.
Please note that you will only be able to install your Android apps on Android devices, i.e. you cannot install an Android app on iOS devices such as iPhones or iPads.