What is the best way to get fro JFK to upper west side manhatten (73rd and Broadway)?

Someone asked the same question a while back and there were some really good answers:
http://www.fluther.com/disc/264/how-do-i-get-from-jfk-airport-to-the-upper-west/

Personally, my preferred method is to take the private bus to port authority and then take the subway or cab from there. If you do that you can get to the upper west for less than $20 and it doesn’t take long at all. The subway is obviously cheaper but it takes a lot longer. Which is fine if you have an iPhone to check fluther while in transit ;)

do you get the private bus downstairs in public transportation? What is it called? My daughter had an iphone so how and why do you check fluther in transit? Unfortunately, I did not get your answer until I got home today. NY was fabulous and I took some shuttle, traffic was thick and we had to drop 8 people off before me. Thank you