Space Stations are NPC-run facilities that allow for trade in a solar system.
To dock at a Space Station, just get within the blue beam of light near the entrance, and a tractor beam will pull your ship in toward the back of the facility, with your ship coming to rest on a landing pad.
Once you have exited your spacecraft, you'll notice two staircases on opposing sides of the station. The one to the right is accessible by all; the one on the left requires an Atlas Pass to enter.
Do not shoot at Space Stations. Doing so results in a fleet of Sentinel attack ships descending upon you rather quickly. Unless you're skilled at fighting off the combatants, there's a very good chance that your ship will be disabled and destroyed. Of course, this means that you get to visit another grave site, but you're okay with that, right?