When you access the state archives for each of the states, there is usually a search box that is provided. Type in, "Military Service Records" to begin your research.
(The link immediately above includes a handy guide to all of the state archives and online digital records)
Access the DAR website, at DAR.org. Click on the green box labelled, "Research you Family History." On the next page, under "Genealogical Research" or "GRS," click "Ancestor Search."
Access the SAR website at SAR.org. In the "Genealogy" tab, in the pulldown menu, select "Patriot Search." Click on "SAR Patriot and Grave Index."
This website includes many of the records for Revolutionary War veterans, as well as their dependents' applications for pensions.
All thirteen of the original states published rosters of their patriots who served in the military. Eight of these state publications are available for free on the internet.
These are: Connecticut, Georgia, Maryland, Massachusetts, New Jersey,
New York, Vermont, and Virginia.
Google search using an expression like "New York Patriots in the Revolutionary War."
The other original states, by the way, are: Delaware, Pennsylvania, North Carolina, South Carolina, New Hampshire, and Rhode Island.
Note: At the time of the Revolutionary War, Vermont was part of New York.