On PC: "C:\Users\<your user name>\Saved Games\The Quest"
On Mac: "~/Library/Application Support/The Quest"
On Android: "Android/data/hu.redshift.thequest/files"
On iOS: You need to use iTunes File Sharing
On PC and the Mac, you can also just click on the "Open Folder" button on the load/save screens.
Save files are compatible between all versions (except the old iOS version). "Save0" is the autosave, while all other numbered saves are the regular save slots.