I got my guns in NYC a few years (8 or 9 I guess) ago (I now live in NJ). I'll tell you what I know and what I've heard.
I'm talking about handguns here, never had a rifle in NYC so I can't comment on that.
When I applied for my target license it took nine months to process. You had to go to lower manhattan (1 police plaza) and file the form in person, they fingerprint you, you supply pictures, and then you wait. Don't call them to ask how it's going, if you do (I'm told) they pull your form out of the pile and put it on top again. When your license is approved you have to pick it up in person. Once you have the target license you can buy one gun, you have to do so with 60 or 90 days, otherwise they pull the license. If you want to buy another gun you have to apply for a purchase authorization, that takes a couple months to process, and again you have 60 or 90 days to make your purchase. If I recall correctly you have to tell them exactly what kind of gun you want (you may even have to provide the serial number, meaning you have to pick it out in advance) and what you want it for. You also had to belong to a gun club if you had a target license. Once you purchase your gun you have 72 hours to bring it back to 1 police plaza for "inspection", with your bill of sale (which they keep, make a copy of it). They record the serial number on your license. A target license allows you to transport the gun from home to the range, in a locked box, ammo seperate. They acted like they were being nice to you, you could go shooting whenever you wanted. Again, if I recall correctly you legally couldn't have the gun loaded at home.
If you get a premise (as opposed to target) license you can again only transport the gun from home to the range, locked up, etc, and you could only do that twice a month on pre-arranged dates. You select two dates (say the tenth and eighteenth of the month) and those are the only two dates you're allowed to take the gun out for practice each month, if you want to change the date you have to do it in writing, and you give up one of the original dates.
If you get a carry license you must know someone.
You renew your license every two years on your birthday (for a couple hundred dollars each time), if you let it expire NYPD WILL be at your home to pick up your guns.
That's it in a nutshell, and again this is a few years old. I've heard that target licenses have been phased out in favor of a "target premise" license, where again you can only take the gun out twice a month. I'm sure the length of time for the license has gotten longer since then. Oh yes, when you go to apply or to pick up your license the folks there try to get you mad, if they succeed you're rejected.
You're going to make at least three trips to 1 Police Plaza, one to apply, one to pick up the license, one to bring your gun for inspection. Maybe another trip to pick up the application (although most gun shops keep a few on hand). Payment had to be made with postal money orders (no bank MO's, personal checks, cash, or anything else).
If there are any specifics I missed feel free to ask, but I think I got everything I can remember. Basically, they make it such a hassle and so expensive that most folks won't even bother, thereby keeping NYC safe