Some games automatically save your progress if you exit the game correctly. If your game has a built-in save feature, such as the Save Stations in Super Metroid, then the game is automatically saved when you use
Start+Select to exit the game.
The instructions here will work for most controllers.
However, If you're using a keyboard or non-standard controller to play games (and can't figure out which button/key is mapped to
R1, etc.), you can change the mappings for these commands quite easily to accommodate your particular setup.
To do this, check out the RetroArch configuration section of the RetroPie wiki.