If you will be making sales in New York State that are subject to sales tax, you must register with the Tax Department and obtain a Certificate of Authority. The Certificate of Authority gives you the right to collect tax on your taxable sales and to issue and accept most New York State sales tax exemption certificates. Generally, the seller collects the tax from the purchaser and remits it to New York State. If you expect to make taxable sales in New York State, you must register with the Tax Department at least 20 days before you begin business. New York State will then send you a Certificate of Authority which must be displayed at your place of business at all times.

There are two types of the Certificate of Authority issued from the New York Tax Department, regular and temporary. The type of Certificate of Authority you need is based on the expected duration of your business activities. The application form and process are the same for two types of certificates.

If you expect to make taxable sales in New York State for no more than two consecutive sales tax quarters in any 12-month period, you may apply for a temporary Certificate of Authority. In determining whether you meet this requirement, keep in mind that the sales tax quarters are: March 1 through May 31, June 1 through August 31, September 1 through November 30, and December 1 through February 28 (February 29 in a leap year). Otherwise, you will need to apply for the Regular Certificate of Authority.

You can apply for a certificate online. Your application will be processed and, if approved, the Tax Department will mail your Certificate of Authority to you. You cannot legally make any taxable sales until you have received your Certificate of Authority.

If you operate a business without a valid Certificate of Authority, you will be subject to a penalty. The maximum penalty is $10,000, imposed at the rate of up to $500 for the first day business is conducted without a valid Certificate of Authority, plus up to $200 per day for each day after.

You must have a Certificate of Authority for each business location. You can choose to file one sales tax return for combined sales at all locations or a separate return for each location. If you plan to operate your business locations as separate business entities, you need to file an application for a separate Certificate of Authority for each location.

A Certificate of Authority cannot be transferred or assigned. If you are buying an existing business, you must apply for your own Certificate. You cannot use the Certificate of Authority that issued to the previous owner.
 
You must also apply for a new Certificate of Authority if you are changing the organizational structure (legal form) of your business, such as switching from a sole proprietorship to a corporation. The new business must have its own Certificate of Authority before it begins business.

https://www.tax.ny.gov/pubs_and_bulls/tg_bulletins/st/how_to_register_for_nys_sales_tax.htm

See also:
U.S. New York State  Individual Withholding Tax Requirements
How to Obtain a Sellers’s Permit in California
United States Sales and Use Tax Guide