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http://www.mta.info/nyct/maps/submap.htm
Board the A line subway at 34th St.: $2
Transfer to the AirTrain at Howard Beach: $5
You will probably need to transfer A lines at Euclid Av.
You want to continue in same direction; ultimate subway (not you) destination is Far Rockaway.
You should buy a $7 card at 34th st station.