[Smilley]

Chrono Trigger uses the EEPROM 64kB savetype. After setting that (and resetting the game for this option to become active), you can save on the world map and at specific save points.
You will also need one of these codes active during gameplay to prevent the game from going into an endless loop during teleportation.

 

[Smilley]

The same thing you'd do if you'd play the game on your DS. Use the game's built-in save feature.