What you actually do in the game is kind of up to you. The whole premise is that you have awakened on a strange planet with no recollection of how you got there. It's just you alone on a desolate planet in a space exo suit. You must explore while your suit finishes re-initializing itself. With a little effort and some tutorial-style missions you manage to get your scanner functional and your mining beam (essential to crafting anything from here on). The game will do a little minor bit of hand-holding to get you moving because you're going to need all of the essentials in order to progress, which includes a space ship.
The game will basically open up to the extent that you kinda have to figure out what you want to do. Some objects you will come across will open some basic side stories. Some of the side stories you will stumble into will lead you off the planet to explore another planet. Some resources are only found on other planets than the one you woke up on. Still further yet, an in-game currency kinda forces you to gather and sell in order to accrue credits, and yet you could spend your time scanning every new thing you come across, because, strangely?, that also rewards you with money...
At some point you will wonder if you should build a home base or take to the stars. It's really up to you, traveler! Do you 100% the world you're standing on, or would you rather see what else is out there in the stars? You can build fun bases on different planets, collect space ships, own your own ship-carrying vessel (own a fleet), become a space trader, become a space pirate, or simply follow the path before you to the answer presented to you at the beginning of the game.
I just recently started playing again, and there are some things that I had wished were more fleshed out. Unlike the CRPGs I grew up with, this one feels quite a bit more open-ended with sporadic, totally random-generated side stories that can be, sometimes, a little immersion damaging when they don't flow perfectly correctly. Still, I absolutely love the style of No Man's Sky, as it takes me back to those old games I used to play. They absolutely should continue to build on this game as it has all the potential to become something truly special.