How does one qualify for the Halo Championshop series?
Players generally don't "Join" the HCS. 343i are yet to announce the 2018 dates but when they do, there'll be LAN events for all regions, most of which are open events so all you need to do is buy yourself a pass when they're available (Team, FFA or Spectator), tag along and there we go! The best so many teams from each regional event qualify for the final of the world championship.
Just like most competitive gaming scenes. You will need to have a team to compete with at LAN/Online events. You will climb the leader boards and or bracket by winning matches. I would say playing and winning at big LAN tourneys is the best route but, online tourneys cant help your team get some light shed on them. Best of luck!