How to get back progress you have made in a game after being deleted?

How do you get all the progress you have made in a game after the game has been deleted and the put back on?

If you've made a backup of your device recently, restore the backup. If not, more than likely, the progress has been lost.

Unless the app stores user progress data in a place that can be restored from, you can't... the app would have to use developer servers, or iCloud to store/back up user data... if the app does that, you'd simply restore a backup made prior to deleting/reinstalling the app.