The website of the New York State Archives is a treasure trove of information in itself, but now it has entered into an agreement with Ancestry.com that makes it even more accessible.
If you go to the home page and then click on “Find Family History Records,” you are taken to a page where you can use Ancestry.com to do a search of many records sets from the state archives. You have to register for a free account, but the instructions are clearly explained on the site.
Note, this does not give you unlimited access to Ancestry, but it does give you free access to this part of it. If you have an Ancestry.com subscription, the New York Archives contributions are already included in any Ancestry search you do.
Start your exploration at New York State Archives Homepage