If you are used to using these same emulators on different platforms, then yes, they work the same. Every emulator has it’s own hot keys for save state and load state, you just have to google what the special keys are for that particular emulator.
Then, in Emulation Station, press Start on the controller and then choose to shut down the Pi (instead of just exiting Emulation Station) and wait 30 seconds before using the switch to power off. When you use the switch to turn it back on, the Pi will power back up to command prompt (or to Emulation Station if you choose to have it start up automatically).
Important note: If you made any changes in Emulation Station (such as changing the name, description, etc. of a rom) you will need to choose to just quit Emulation Station and go to the command line or else it will not save the changes.