By Subway
This area has relatively poor subway coverage compared to most of Brooklyn. There are no subways to the Flatlands area--the closest station is Flatbush Avenue-Brooklyn College on the 2 and 5 rush hours only--almost an hour away by walking though buses along streets like Flatbush Avenue and Avenue H can bring you there faster!
Canarsie is somewhat better served, with the L terminating at Canarsie--Rockway Parkway, which is about 25 minutes away from Jamaica Bay by walking though the B42 bus goes to Canarsie Piers from the station. The L is somewhat difficult to access from elsewhere in Brooklyn, but the G, M, J/Z, and A/C all have transfers to it.
On the other hand, if you're visiting East New York, probably the area of least interest to travelers due to the high crime, you are spoiled for choice. The 3 terminates at New Lots Avenue, the closest station to the Bay but once again, still a distance. The A/C and J/Z also have lots of stops in East New York. If you're traveling directly to Brooklyn from JFK, you will probably pass through here--rest assured, the trains are safe.
By Lirr
Long Island Railroad's Atlantic Branch has a single stop in this district at East New York. Trains stopping here are heading to or originate from Atlantic Terminal.
By car
Given the spotty subway coverage and high crime in some parts of this area, East Brooklyn may well be one of the few places best reached by car. The Belt Parkway and Shore Parkway circle Brooklyn and are very close to the attractions in the Jamaica Bay.
By bus
The BM1, BM2, BM4, and BM5 express buses come here from Manhattan.