Generally no special rules, other than your standard administrative stuff like getting a business license and having enough capital to get up and running. I'd mention stuff you would need for a business loan, but those are pretty scarce right now.
It also depends if you organize as a sole practitioner, LLC or a subchapter S corporation. But those are things you should discuss with an attorney/accountant and decide what is best for you. If you are asking about marketing to the same Client base as the employer, I can tell you in the US that even if you have signed a non-compete agreement, and even if the non-compete agreement meets all the rules about limiting range, time frame, etc., that in court, those non-competes are struck down except in the rarest of cases. Grab the Clients you can. But bear in mind that many corporations (and smaller companies owned by ex-spouses) rely on fear and financial intimidation to protect their interests. Best bet is to stay under the radar so that you are never forced to defend yourself.
"If you are going to walk on thin ice, you might as well dance!"