As it stands this moment, ED's singleplayer/multiplayer setup is as follows:
1) The game uses 32 player max instances, it is rare to see more than 4-5 actual humans at a time though.
2) The game uses 3 main modes, solo, private and open. Open mode allows you to come across any player in the game, this is the mmo-ish mode. Private group works the same as open, except the only people you can run across are other players in the private group. Solo makes it so you will never encounter another player, but it is still online like the other 2 modes.
3) The game does not have any coop functionality. There are no chat channels and no ability to form a traditional group/party/squad. However the friends list will cause the instancing engine to attempt to put you and your friends in the same instance if possible. As such, you will see your friends at stations, nav beacons and other common points provided you are both in the same spot. The system will not tell you their location or mark them in any special way so coordination must be done via an external program such as TS3.
It is possible to play cooperatively with these limitations. I was mining with a friend in a resource extraction site earlier. Though we both had to travel to the same location manually and coordinate it via TS3, we were able to get to the same location and instance with 100% reliability. This also worked when traveling back to the station. So common sites are not a problem, you can definitely play with friends there in open or private modes. But there are some locations that aren't common such as unidentified signal sources (USS's) and anything involving an interdiction (same idea as drag bubble if you ever played eve though completely different mechanically). These client unique sites do not directly allow for you to play with friends. There is a work around involving a FSD scanner, but it's slow and a pain to use for this purpose.
As for single player, hop into solo and never see another human if you wish. Alternatively, run off into the far side of the galaxy. With around 400 billion systems, it's easy to disappear.