you can take the 4, 5, 6. The J or Z to the estation brooklyn brige/city hall. You arrive at the bridge across the street from the subway station
No train goes over the Brooklyn bridge, but BDNQ trains go over the Manhattan bridge that is parallel so you can see the Brooklyn one like that. To walk the Brooklyn bridge, as Azael said take some train close to it and walk.
Also train 2 or 3 and stop at park place station, cross the square and begin the bridge.
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