From Upper West Side. to JFK airport.

1. Walk to Broadway and 79^th Street.
2. Go down the “Downtown 1” subway next to the church. (30-60 sec)
3. Swipe through the turnstile and wait for a train. (~10 min)
4. Get on the train when it arrives. (10 sec)
5. Don’t get off at 72^nd. (1-2 min)
6. Don’t get off at 66^th. (1-2 min)
7. Get off at 59^th (also called Columbus Circle) (10 sec)
8. Follow the signs to the A (downtown (may also say Queens or Brooklyn)).  Don’t go through any turnstiles. The signs will lead you down the stairs to the platform. (45-90 sec)
9. Wait for the A train that says Far Rockaway or JFK airport or Howard Beach.  [NOT Ozone Park nor Leffers Blvd.] (10-15 min).  You can also get on a C train, but it’s worth waiting for the A since the C makes many more stops.
10. Get on the train and get comfortable. (10 sec)
11. This will be a long ride.  You’ll probably see other people with suitcases.  You’ll know you’re getting close when the train goes above ground.  I think this happens around 80^th or 88^th.  Get off at Howard Beach/JFK stop.  (45-60 min)
12. Follow the people up the escalator, over the tracks, and you’ll see large turnstiles that are built for luggage (it actually doesn’t ‘turn’). (1-2 min)
13. You now have to buy an Airtrain ticket, which is actually just a Metrocard (subway) ticket with $5 on it.  Use one of the automated machines to buy the $5 (Airtrain) ticket. (1-2 min) (A regular monthly or weekly subway ticket will not work.)
14. Use the ticket to swipe through the big turnstile and go the right/forward and wait for an Airtrain.  Find out which terminal (1, 2, 3, 4, 5, 6, 7, 8, or 9) you need for your airline.  Get on the train going towards your terminal. (I think that from here, all trains go towards the terminals) (2-5 min)
15. Try to keep apprised of which stop the Airtrain is making.  You don’t need the first few. (10-15 min)
16. Get off at the correct stop and follow the people.  From there, try to find the check-in counter for your flight.

From JFK airport to the Upper West Side:

1. Get off your plane.
2. Follow signs to the Airtrain.  You’ll probably have to go up an elevator or an escalator.
3. Wait for an Airtrain going towards Station A / Howard Beach. (5-7 min) . . . The Airtrain is not a well-designed system. Pay attention. There is an inner loop that goes to "all terminals" and goes arround in circles forever - don't get stuck on it. Then there's an outer loop that has two possible final stops: Station D Jamaica, and Station A Howard Beach. Listen to make sure you get on the right train.
4. Listen for the announcements, but since you’re getting off at the final stop, you don’t have to worry much about missing your stop (It’ll be clear when almost everyone left on the train, gets off.) (10-15 min)
5. Get off at Station A / Howard Beach. (10 sec)
6. Follow the people to the ticket vending machines.  Buy a Metrocard (subway) ticket for at least $7.  This will probably be presented as an option such as (Airtrain+subway).  A monthly/weekly card will not work here.  If you have one, buy just a $5 card instead of 7 and see the next instruction. (1-2 min)
7. Swipe with your card at the oversized luggage turnstile (it doesn’t actually ‘turn’).  Go throught the ones that let you go to the subway, not the street, as indicated in the picture.  This will take $7 off your card.  If you only bought a $5 card, go through the street turnstiles, and then use your other (monthly/weekly) card to go through the normal turnstiles. (30 sec)
8. Go down the stairs to the A train to Manhattan. (30-60 sec)
9. Wait for the first train that comes. (You can’t go wrong) (5-15 min)
10. Get on the train and get comfortable. (10 sec).
11. This will be a long ride.  You’ll know you’re getting close when you stop at Penn Station and then at Times Square. (45-60 min).
12. Get off at 59^th street to transfer to the 1 train. (10 sec)
13. Follow the signs to the 1 uptown train. The signs will lead you up some stairs. (30-60 sec)
14. Wait for the 1 train and get on when it arrives. (5-10 min)
15. Don't get off at 66th nor 72nd. St. (5-7 min)
16. Get off at 79th Street. (2 min)

Advanced options:

Starting at step 11, you can try to make your trip more efficient as follows:

• As soon as the Hoyt-Schermerhorn station, you can start the following: Every time your A train stops at a station, look across the platform to see if a C train is arriving at the same time. If it is, grab all your stuff and quickly get off your A train and onto the C train across the platform. (If this fortunate circumstance doesn't happen by the time you reach 59th street, follow instrucitons 12-16 from above.)
• Now that you're on a Uptown (or Manhattan bound) C train, you can just wait and get off at 81st street (Museum of Natural History) Stop.

The reason this is desirable is that you do not have to go up any stairs, nor wait for the 1 train, as described in steps 13-14. The reason it's advanced is that the C trains run rather rarley (no alliteration intended). Therefore, you shouldn't get off your A train unless you already see the C train across the platform.

As a final warining: this is New York, and though you'd expect the train conductors to wait for people to rush across the platform between the two trains, there's no guarantee that they won't close the doors on you before you make it. If that happens, you just have to wait for either a C or and A train, and continue on your way.

A note for visitors on buying metro cards:

The vending machines are pretty user-friendly, if you know what all the different options mean. You'll have a chance to buy and unlimited card that lets you travel all you want for a day/week/month. You also have the option of buying a regular money-valued card. The unlimited ones are generally not worth it. They're only good for people who regularly commute to and from work (and even then it's not that big a savings.) So I'd recommend getting a money-valued card at about $10 or $20. They don't expire, and you don't feel bad when you decide to take a taxi with your fiends because you already 'paid' for unlimited subway rides.