Assistance to understand the First Departemnt of New york supreme court

I want to file an appeal. I have been told that if I do so the sitting will occur in the first department of the court of appeal in New York. I will truly appreciate it if someone could provide me information regarding the appealing process and decision making in order to understand if I have any chance. I would like to understand the exact process of appealing, who are the relevant people making the decisions and any other information you find necessary.