How to save your game in Kingdom Come Deliverance is covered on this page. It doesn't work the way many RPGs do, so it can be a bit confusing if you don't know what you are doing.
How to Save Your Game
The game saves automatically when you start a new quest or advance to an important event. You can save your game manually but this can only be done by sleeping in your own bed, visiting a bathhouse, or drinking Saviour Schnapps. Saviour Schhapps can be either brewed by Alchemy or bought from an innkeeper or most general traders. Be sure to always keep at least a couple with you.