You stand still. See.
Running out of ammo in Destiny? Just stand still, as you can see in the video below.
I've just tried this and it's true. I blasted off all my primary weapon ammo and stood there, and after a short wait it was replenished. I also got some secondary ammo as a bonus.
Check it out, and be sure to bookmark our Destiny guide for all the Gold Chest and Dead Ghost locations, Strike walkthroughs and more.