There really isn't a "process" other than just cancel your Citi card then go join the AC via normal means.
I suppose you could call to join but I don't see any reason why you wouldn't just do it online.
And doing it this way you will be treated as a new member (AFAIK) although the price difference is only $50 now for a new member vs. renewal.
So you're basically spending 75k miles to save $595. Pretty bad use of miles IMO.