How many ways can I tell people about my cleaning business?

That is a huge area, what type of cleaning, residential? Commercial? Both? I would suggest you get known in a much tighter area. Like where you are going to live. Not many residential cleaners in Brooklyn going to Montvale, NJ.
Likewise, not many deck cleaners going to the Bronx. See?
Start there, with your new home.

GordonJ

Same way you got known in Georgia.

Really. What did you do to get known in Georgia? What worked best there?

If you just need a list of marketing methods...

in no particular order:
joint ventures
SEO
banks that have a lot of foreclosures coming up and need left-over furniture and trash in those foreclosed homes taken out
apartment building management companies
office building management companies
direct mail
ads in local newspapers
fliers in rich(er) neighborhoods
radio ads
TV ads
all kinds of ads.

By the way, it's easier and more profitable to run a small fiefdom than a large one. Tri-state sounds big, daunting. Why not start with a smaller part of tri-state? When you're top dog there, you attack the next small part.

You can also use one of the Proximity devices which are now available . Just Google search . I don't want to put a link here . Very effective for getting eyes on your site ,especially for local businesses .
You are able to broadcast messages to Android phone users within 100 yards of the device .
Once you arrive in your new area , you simply carry the device with you and it does the work for you .

Countless ways really. Through the internet: blogging, social media marketing, youtube marketing. Think of how you can shout out your cleaning business, then brainstorm content ideas for a few platforms. You'd want to speak to an SEO pro to get your local search game tight.

My wife and I have cleaned for 17 years.

There must be some reason that you're moving, so I'm assuming you know someone there. Step one would therefore be networking.

Newspaper ads are fine, but you could also make use of sites like Craigslist, Thumbtack, etc.

If you need quick work in bulk, property management companies may need help.

Once you get your first clients, ask for referrals. Do such a good job of under promising and over delivering that people can't help but tell their friends about you. Take a personal interest in your clients.

I have a friend on Long Island that has a cleaning business and he may need contract help.

As far as registration with the state, if you're registered with Georgia it makes sense that you'd have to register again with your new state. I don't know the legalities though.

I have a feeling that you're going to have a different type of clientele to learn. Congrats on the new adventure. Cleaning has been good to my wife and I for a long time.

You can't always be there to chat with website visitors - you have to sleep after all! Luckily live chat software like Pure Chat allows you to turn your chat box into a lead capture form when you're not available to talk in real time.

Make yourself accessible on social.

Considering that 78 percent of respondents in this survey say that a company's social media post impacts their buying decision.

Though blogging, social media marketing, youtube marketing etc. there are countless ways.