By bus
Brooklyn is covered by an extensive network of MTA buses, for which a map is essential (http://mta.info/nyct/maps/). Of particular note is the B51 bus, which runs between City Hall in Manhattan and Smith St./Fulton St. in Downtown Brooklyn, via the Manhattan Bridge. The trip is particularly beautiful on the way to Manhattan because of the skyline. Note that the bus operates only on weekdays, with the last bus leaving Smith St./Fulton St. at 7:10 P.M. and from Park Row at 7:40 P.M., according to the current schedule and depending on traffic. See the MTA website for bus maps and schedules of individual bus lines. The B39 travels over the East River on the Williamsburg Bridge between Manhattan and Brooklyn. Another route of note is the B15, which runs between JFK Airport and the Woodhull Hospital in South Williamsburg. Service on that route is provided around the clock. Possibly the longest mostly straight-line bus route in Brooklyn is the B41, which runs nearly the length of Flatbush Avenue from the line's northern terminal near Borough Hall just west of Flatbush Avenue itself to Kings Plaza at Avenue U with a branch to the Mill Basin and Bergen Beach areas, about 9 miles away. Other long routes run a limited-stop service that stops at major intersections and points of interest. Limited-stop service is provided on the B6, B41, B44 along Nostrand/Bedford Avenues, B46 along Utica Avenue, and B35 along Church Avenue. That pattern is in effect from around 6 AM to 10 PM daily on these routes 5 AM-11:30 PM on the B46. The B49 has southbound limited-stop service on weekday mornings, mainly tailored for college students traveling to Kingsborough Community College. The B103 is a limited-stop route between Downtown Brooklyn and Canarsie, which runs on weekdays, Saturdays, and Sundays.
One can also take express buses, with an X prefix, to/from Manhattan $5.50 one way. Most express buses serve Southern Brooklyn, for the most part an area that's somewhat subway deprived, especially to the east. The X27 and X28 run daily from around 6 AM to 11:30 PM. Other express routes run every day except Sunday and have a BM prefix.
By Subway
Brooklyn is well served by some 18 subway lines, most of which provide direct service to Manhattan, Queens, and the Bronx. The sheer size of the borough does make it harder to identify the fastest route - it is best to download a subway map from the Metropolitan Transit Authority's website (http://www.mta.info/) or pick one up for free at what New Yorkers still anachronistically call a token booth, even though tokens are no longer on sale or used in the New York subways.
Getting into Brooklyn by subway from Manhattan is easy. Pretty much every line goes through Downtown Brooklyn and stops at Atlantic Avenue, the largest subway stop outside Manhattan. From here, you can transfer to pretty much any subway besides the A/C, J/Z, L,F, and G to get to your destination in Brooklyn. You can also walk about two blocks north of the station to find Fulton Street G and Lafayette Avenue C. To use these, though, you have to pay another fare, currently $2.25, or just have an unlimited rides card.
There are 3 lines you can take to get directly from Queens to Brooklyn. The A goes from the Rockaways in Queens through the eastern edges of Brooklyn into Bedford-Stuyvesant and finally Downtown Brooklyn before continuing in Manhattan. You can also transfer to the C for local service. Beware taking this route at night, because it passes through some rough neighborhoods, including East New York.
The J/Z goes from Jamaica in Queens near JFK; take the AirTrain to Jamaica through Williamsburg. It goes through many of the same rough neighborhoods as the A. The M travels from central Queens through Williamsburg while conveniently avoiding the rough neighborhoods that the J/Z goes through but inconveniently ending up in an isolated neighborhood with little interest to tourists.
The final choice is the controversial G, which snakes from Long Island City through Williamsburg and Downtown Brooklyn before ending near Prospect Park. Although it may look like the best way to get from Queens to Brooklyn, it is notoriously slow and irregular, and sometimes lines that go through Manhattan are faster. However, the G does serve some areas relatively unserved by other subways. And even though the trains are a bit grungy and the stations dilapidated, the G doesn't go anywhere really dangerous.
The L also goes into Queens from Brooklyn but so briefly that it's not a practical option for getting between the two boroughs.
The Q train travels from Coney Island to Midtown Manhattan, passing through Sheepshead Bay, Kings Highway, Midwood, Kensington, Park Slope and South Brooklyn, and parallels the main roads of Ocean Parkway and Coney Island Avenue. It also stops at the main transfer stations of Atlantic Avenue, 14th Street -Union Square, and 34th Street, making it easy to transfer to other main lines, including the B, 1, 2, 3, R, J, M, and Z trains.
The F train route is very similar to that of the Q train except that its stops are on the opposite side of Ocean Parkway.
By Lirr
The Long Island Rail Road (http://www.lirr.info/) has a major station at Atlantic Terminal Atlantic Avenue subway station, which is accessible from the Atlantic Avenue/Pacific Street combined subway stop, served by the 2, 3, 4, 5 on weekdays, B on weekdays, D, N, Q, and R lines and near the Lafayette Avenue station of the C train and the Fulton Street station of the G train. Other LIRR stops in Brooklyn are Nostrand Av. at Atlantic Avenue served by the A and C subway lines a few blocks away on Fulton Street and East New York served by the A, C, L, J, and Z a few blocks away at Broadway Junction and the L at Atlantic Avenue, though Broadway Junction is probably a safer bet. Eastbound trains continue to Jamaica Station in Queens, from where passengers can change to most LIRR lines for points further east or take the AirTrain to John F. Kennedy Airport JFK. The LIRR no longer runs in Brooklyn during late nights midnight to around 5 AM, so to get to JFK from Downtown Brooklyn then, you have to take the A
By ship
The 'Water Taxi,' at Fulton Ferry Landing (http://www.nywatertaxi.com), provides service from various points in Manhattan along the East River. The Water Taxi recently added service between southern Manhattan and Red Hook, intended for customers of the newly built Red Hook Ikea but available to everyone.
By car
The connections between Queens and Brooklyn are too numerous to mention, because the two boroughs share a land boundary, so almost every street on the border just continues into the other borough. Prior to 1990, the street signs in each borough had different colors, but they have since all become green - with the exception of brown signs for historic streets - and can no longer be useful in distinguishing between the boroughs.
The Williamsburg, Manhattan, and Brooklyn Bridges link Manhattan and Brooklyn, and the Verrazano-Narrows Bridge links Staten Island and Brooklyn. Only the Verrazano is a toll bridge. There is also a toll tunnel, the Brooklyn-Battery Tunnel, which links Brooklyn with the Battery the southern tip of Manhattan.