Since I am a seat holder (prices definitely was a little below 2.5M then), let me describe the basic process.
First thing you need to do is to form a clearing relationship with a CBOE clearing firm. Look it up (or call CBOE) to get a list of clearing firms.
Then you will need to do a membership application process, which requires your bank to verify your assets, history of income, trading experience, etc. It helps to have your personal attorney here.
You will need to either form a new Broker / Dealer, or (much easier), buy an existing (but defunct) B/D "shell". Regardless, one member of the firm (most likely you), will at minimum need to be holders of Series 4 and 24 (securities market principal).
CBOE will most likely want a sit down "interview" after the application was submitted, mostly to make sure that you have working knowledge of the options industry. I did it over the phone, but then a lot of ppl in the market governance committee knows who I am.
After the application gets approved, it takes about 2 months (at fastest). Then you will submit a "bid" for the seat market, guaranteed by your clearing firm (most likely by cash account balance, unless you hold other securities or say a Merc seat with them). And once the seat prices are "matched" (after negotiation) and money goes thru (don't worry, almost all clearing firms have a Seat person that will help you with the bid process). Congratulations, you are now a seat holder. Now the hard part begins.
The same application process (but not the bid / match process) applies for prospective seat leases.