All, first post here so don't flame the newbie. I've just got a P3P and have yet to take her out.
I happen to be a Private/Commercial rated active pilot so can explain a little more and answer some questions.
There are no Class A airports. Class A is above 18,000ft.....
Here's a link to SkyVector NYC "Sectional" chart of New York:
SkyVector: Flight Planning / Aeronautical Charts
NYC Airspace is one of the more complicated layouts in the country. There are three major airports (JFK, La Guardia and Newark - KJFK, KLGA and KEWR respectively) and then additional corporate and smaller airports (Teterboro, Morristown, Westchester, Essex County and Farmingdale - KTEB, KMMU, KHPN, KCDW). Further out to the East, you also have Islip (KISP).
Any airports marked on the map with a blue dot or blue runway layouts have associated airspace. Any purple airports marked are airports but don't have FAA controlled airspace around them.
Obviously, JFK, Newark and La Guardia are major airports (technically Class B airspace). Here's a link to all Class B airports:
List of Class B airports in the United States - Wikipedia, the free encyclopedia
Class B airports generally have the inverted wedding cake layouts referred to above. Let's look at JFK. Immediately around the airport you can see a notation on the chart of 70/SFC (it'll be 70 over SFC on the chart). This means the airspace bounded by the thick airspace lines is defined from the surface up to 7,000ft. Now look just to the south of JFK and the shoreline. That airspace is marked as 70/+05 meaning that this small portion bounded is airspace that is restricted from 500ft up to 7,000ft. Move further out (south) into the bay and you see the notation 70/+15 so that means restricted airspace from 1,500ft up to 7,000ft. You have to look quite hard sometimes to see exactly where the boundaries are but you can work it out.
Class C airports don't have quite as extensive airspace but it's common to have the same kind of inverted wedding cake layouts. Look at Long Island Mac Arthur on Long Island to the East (airspace is purple). Same notations for altitude.
Class D. Let's use my home airport of Essex County (KCDW) to the NW of Newark (KEWR). Class D airports generally have operating control towers and the airspace is a simple cylinder around the airport. Look for the blue dashed airspace around the airport. Inside the blue dashed ring you'll see a notation of "[27]" that means the airspace is effective from the surface up to 2,700ft (Mean Sea Level). As a side note, Class D airports often shut down overnight and the Class D airspace is also inactive (this varies by control tower). If you're in any doubt that some of these airports are small and not busy, let me put that to rest. Teterboro airport near NYC is a Class D but averages 470+ operations per day and most of these are private jets - so not small aircraft (think Gulfstreams etc).
Another complicating factor is that all the altitudes are adjusted for barometric pressure - all planes have altimeters that can be adjusted.
Lastly, here's a link to the FAA Airspace publication.
Clear? I'd be happy to answer a few questions. Obviously, the above doesn't count as formal training but gives you an idea of how the airspace is mapped out on a 2D chart.
I fall at about 4.5nm from KCDW so I'll be having a chat with my local controllers in the near future to see what they want to know. Technically, the airspace I'm in goes from the surface up to 2,700ft so even flying @ 20ft I'm violating the airspace (seems crazy doesn't it!).
Cheers,
John