A Last of the Galilean game can be saved in the normal way, by pressing Esc, then Save Game.
However, loading a game is not quite so simple. To load a LOTG saved game, first use the Last of the Galilean menus to load the mission you saved the game from (for example, if you saved a game on "Ganymede Evasion", you need to start up that mission). Once it loads, press Esc, and select Load Game from here.