You can save ONLY at a space station. SAVE EVERY CHANCE YOU GET!
You do it by purchasing "Salvage Insurance", under Resources, use the right arrow to buy 1; when you Enter you'll see a list of 10 game slots.  Pick a slot and press Enter again. This list shows when you saved and what sector.

(Tip) Use more than one slot, and alternate.  Then when a catastrophe happens, you can go back to before you screwed up.

(Tip) You can't save at the Space Equipment Dock, the Shipyard, or any of your own stations.  If you're shuttling between these, dock at a normal station along the way and save.