Checking with someone who has a permit, here is what I have been told about all this. There are two types of licenses in NY (maybe another one too for a work related type). There is a restricted permit (hunting and target shooting) and a concealed carry permit. Both need 3 personal references, address history, at least 21 years of age, a mental health check, picture for the ID, full finger prints and an FBI background check. It takes from 3 to 6 months to process. As I understand a retailer won’t let you touch a pistol or purchase ammo unless you have a license. Each purchase must be approved by a judge before you can get the pistol. It takes about 2 or 3 weeks to get a new or used pistol.
Good thing we have all those regulations to protect us from stuff like this.