By Taxi/Yellow Cab or Uber (DO NOT take any car service who approaches you in the airport )

The cost varies, depending on time and traffic. It could be around $45-$55 plus 10-15% tips. 

By Bus/Subway Train

LGA is not connected with any Subway Stations. Also there is no subway train runs from Queens to Brooklyn.
It will be a bit of an extended trip through Manhattan, but enjoy the exploration! (It might take more than 1 hour and 30 mins) 

Take Q70 LGA link bus to Roosevelt Av/74 St.
Transfer to F train. Get off at Delancey St.
Transfer to J train to Brooklyn. MTA cost: $2.90 per ride(with transfers), or $34 for weekly pass.

Get off J train at Kosciusko, you will see a supermarket on Broadway and Kossuth Pl.
Make a left turn at Kossuth Pl, walk 1 block to Bushwick Ave.
Turn right at Bushwick Ave, walk 2 blocks towards Van Buren St.
You will see the building is at the corner of Bushwick ave and Van Buren St.