What is a State Supreme Court Justice:
State Supreme Court Justices rule on civil cases over $50,000, as well as matrimonial cases, contracts and felony cases (Felony cases in NYC only). Despite the name, it is not the highest court in the state and each county has its own elected Supreme Court.
State Supreme Court Justice candidates are not selected through a party primary, but rather are nominated at a convention by elected Judicial Delegates. In New York, a Judicial Convention is the only way a person can be nominated for State Supreme Court.
What is a Judicial Delegate:
A judicial delegate is a person who is elected to represent their Assembly District at the Judicial Convention. In most districts, one party has such an overwhelming advantage that this process essentially decides who will be elected.
Judicial Delegates are elected in the June primary and attend the Judicial Convention in August. They must petition to get onto the ballot, usually as part of a slate put forward by one or more Democratic Clubs, though anyone who meets the qualifications can petition and run for the position. To run for Judicial Delegate in Manhattan, you must be a registered Democrat in the county.
For a more detailed explanation of the process, you can read “What is a Judicial Convention Anyway” , a document created by the Four Freedoms Democratic Club.