You have to remember that many games (especially console games) will enforce aim assist even if you specify it off (in these games the aim assist is simply weakened when 'off').
Aiming in games simply comes down to practice. Before hitting the multiplayer games, it might help to go into a game like Blockland or Garry's Mod, spawn a bunch of objects at different rangers, take a gun and try hit very specific spots on the objects. Set up a points system that nets you more points for accuracy. Do it a couple times a day, and watch as your average score increase.
When you're good at stationary aim, then make the target move. Then you need to start moving. Increase the stakes the more you try. You might also want to enter Casual CS:GO matches to help you get more "real" practice without worrying about your ranking going up or down.
Really though, I wouldn't put too much worry onto using tools like "aim assist" or "mouse acceleration" or whatever. People will use whatever they can to make themselves sound better, and yet probably have expensive mouse setups with buttons that let them change sensitivity on the fly and won't consider that the same. At the end of the day, it's just about practising with the tools you have and having fun with what you're doing.
