There are 4 steps for that. The first is to complete the application.
What is the application name?
The application is called a Standard Permit , Driver License for Non - Driver ID Card PDF [ 2 ] MV-44.
What is the second step?
Determine what you need for identification at the DMV. You would need to complete this guide to know what you need for identification if you wan a REAL ID or an Enhanced ones.
What if I just wanted a Standard ones?
For the Standard ones that only display " NOT FOR FEDERAL PURPOSES ", you would just need your current NY State license as proof.
So i only need that as proof of identity for the Standard ones?
Yes. You are correct.
What should I do if i do not have a New York State driver license but still wanted to drive a taxi or livery vehicle in New York City?
First you need to get a Class E driver license instead of Class D. Then, you would need to contact the Taxi and Limousine Commission [ 6 ] and take not that from October 2020 onward, to board a domestic flight, you  will need an Enhanced or REAL ID unless you already have a passport.
Could i just use the Standard ones for traveling?
No. After October 2020, you would need an Enhanced or REAL ID.
How can I know what type of ID that I have?