How do I heal my ship in No Man's Sky?

Quitting the game and starting up again seems to have done the trick. My ship was back to 6 little health icons when I did that.

Note: In this case my game actually crashed (because PS4), so I'm only assuming that quitting the game would have had the same effect. (The save point that reloaded was from a couple minutes before the game crash, which was several hours after my ship was damaged.)

At the very least, you can talk to the NPC in a space station, and providing you have the appropriate rank with them you can ask them for repairs, which should repair your ship.

I've noticed when docked at a planet based trade station (a multi platformed one) that when I went back to my ship the damage was repaired. Earlier in the same play session I'd stopped at a space station in hopes of recovering ship health and it didn't happen. I don't often get into ship combat, and when I do I usually die, so this is the only instance of ship repair I can account for. Not sure if this was the actual cause for repair or if traveling a good distance (shields maxed, like how your health recovers) had played a factor into it, but I'm pretty sure it only happened after visiting the planet trade station. If you encounter a similar experience I'd love to know. Hope this helps.