There are several forms and procedures if you must move to NYC from Canada. But do not worry, I am going to review some important things you will be needing if you want to move to NYC from Canada.

You need proper preparation before moving to NYC from Canada
Moving to NYC from Canada Requires a Visa
Where To Live When You Arrive
Visit New York Before Moving There
Setting up your Banking and Credit
Canadian citizens do not need a visa to enter United State directly from Canada for the purpose of visiting or studying.
Canadian citizens traveling to the U.S. by sea or land must have Western Travel Compliant (WHTI), and all Canadians entering the United States by air require passports.

However, some Canadian need Visa before they can U.S.
Example: Intending Immigrants, investors, or fiance/fiancees must provide a visa before entry in the same manner as other nationalities. Refer to this post[1] to continue reading
https://passiveguides.com/your-guide-to-moving-to-nyc-from-canada-2022/