Can you get to Brooklyn by subway from the LaGuardia airport?

There is no subway near LaGuardia Airport, but the M60 bus runs to/from LaGuardia, and you can take it to the subway.

You can take the M60 to Astoria Boulevard and 31st Street in Queens, and transfer to the Astoria Boulevard station on the N or Q trains (of the N-R-Q, the yellow line). Both the N and Q go to Brooklyn.

Or you can take the M60 to 125th Street and Amsterdam Avenue in Manhattan, walk 2 blocks east to St. Nicholas Avenue, and transfer to the 125th Street station on the A and C (of the A-C-E, the blue line) and B and D (of the B-D-F-M, the orange line). The A, C, Band D all go to Brooklyn.

Or you can take the M60 to 125th Street and Lenox Avenue in Manhattan, and transfer to the 125th Street station on the 2and 3 express trains (of the 1-2-3, the red line). Both the 2 and 3 go to Brooklyn.

Or you can take the M60 to 125th Street and Lexington Avenue in Manhattan, and transfer to the 125th Street station on the 4-5-6 (the dark green line). The 4 and 5express trains go to Brooklyn.

See the Related Link below for an M60 bus schedule.