In Farming Simulator 19 the game automatically saves at intervals of 5-10-15 minutes - you can change this setting in the game options, or turn off the auto-saves. The game also saves itself when you open up the menu, if you haven't done it for a long time - the screen will show information that save has been made.
You can also save the game manually: open the menu and go to the last tab (with instructions). At this point you can save the game manually by pressing Space (X on XONE / square on PS4). You cannot save the game in another save slot.