1 - Set up a hardware VPN between sites using something like Cisco routers (If you don't want any trouble from them use Cisco - use cheap routers if you do)
The connection is down to you, Megastream, LES10, ISDN, Frame Relay - It depends on the costs of these technologies where you are and what's available - speak to telcos in each area).
Each site LAN will have its own IP range which needs coding into the VPN access points so that the server on site 1 can ping the other servers via the WAN and vicaversa.
You may also want the LAN PC's to do this too.
2 - If your remote servers are already AD controllers you'll need to demote them (Not required if you are happy to work on domain trusts in AD but this won't give you a single domain which I would suggest is easier to handle) - Use dcpromo and let it do it's stuff.
3 - Promote each server on the remote sites (Using dcpromo command prompt). When prompted, each server needs to be added to an existing domain - give it your NY domain name and a Username/Password that has sufficient security rights - Admin account or whatever)
4 - Wait until the server has been promoted (This will include it setting up various bits and pulling a copy of the AD structure from the NY domain - it'll also set up AD replication so that changes to AD on one server will migrate to the others)
5 - Set up new user accounts on any of your new AD Servers - it's all one now. These accounts will replicate over your network so all servers will have a copy of them.
6 - Migrate users data from their old user accounts and hand out user names and passwords.
Ok - so that's a fairly simplistic approach - You'll need to have at least one DNS server set up, there are bandwidth complications (How fast are the links between sites? Is it worth running DNS on other sites too? Will you store user data on individual servers or use DFS to store a copy on each server?). There is so much more to go in to than just plugging it all together.
Hope that helps a bit though.
It's not to be undertaken lightly as something like this is a fairly big project that needs managing extremely well to pull off correctly. Cheap links between sites will wreak havoc on connectivity, expensive links won't but you may be paying more than you need. Balance in all things!
You'll need SLA's from a variety of companies, the Telco which provides the link - the guys that install and set up the routers, whatever you have in place for the servers etc. etc.
Start with a network diagram and go from there!
I do this whole thing for a living and am happy to project manage the lot for you if it's for real. At a price of course :-)