Take the 2 train. The 2 train stops at 34th Street-Penn Station (at 7th Avenue).
The 5 train (of the 4-5-6, the dark green line) does not stop at 34th Street. Instead, you would have to transfer to the Downtown 6 at 42nd Street-Grand Central Station, and take the 6 one stop to 33rd Street (at Park Avenue South).
Although, if you are going very far east on 34th Street (like, 3rd, 2nd or 1st Avenue) then you may want to take the 5 and transfer to the 6, because the walk from the station will be much shorter. The 1-2-3 line runs on the West Side, while the 4-5-6 runs on the East Side.
I am assuming you're referring to Fulton Street in Manhattan (there is also a Fulton Street in Brooklyn).
It depends on where on 34th Street you are starting out from. I will list your options from easternmost to westernmost:
34th Street at Park Avenue: the 4-5-6 (dark green line)Take the Downtown 6 local train from 33rd Street (at Park Avenue) to 14th Street-Union Square. Transfer at Union Square to the Downtown 4 or 5 express trains, 2 stops, to Fulton Street (at Broadway).
Depending on which exit you use, you may exit at Fulton Street or the next street down (Dey Street).
34th St at Broadway (Herald Square): the N-R-Q-W (yellow line)There are a few different routes you can take if you're starting out from Herald Square. You can take the Downtown R local train all the way there, from 34th Street-Herald Square to Cortlandt Street (at Church Street, on the east side of the WTC site).
Cortlandt Street is 2 blocks south of Fulton Street. There are 2 entrances/exits to this station: 1 in front of Century 21 (between Cortlandt and Dey Streets) and 1 in front of the Millennium Hilton (between Dey and Fulton Streets).
OR, you can take the Downtown Q express train, 2 stops, from 34th Street-Herald Square to Canal Street, and transfer at Canal Street to the Downtown R local train, 2 stops, from Canal Street to Cortlandt Street. This will cut your number of stops from 8 (taking the R the whole way) to 4.
If the Q train comes first, then I'd take it and transfer to the R at Canal Street. But if the R comes first, I'd take it and just go local all the way.
OR, you can take the Downtown Q express train, 1 stop, from 34th Street-Herald Square to 14th Street-Union Square. Transfer at Union Square to the Downtown 4 or 5trains to Fulton Street. You will have to take this route if you're traveling between 11 PM and 5:30 AM, as the R train does not run during those times.
Unless you have to, I wouldn't transfer to the 4 or 5 at Union Square. It's easier to stay on the same subway line, because then you don't have to walk through the station to another platform. The Downtown Q and R will stop on the same platform. You'll have to walk to the other side of the Union Square station to transfer to the 4 or 5.
34th Street at 7th Avenue (Penn Station): the 1-2-3 (red line)Take the Downtown 2 or 3 express trains, 4 stops, from 34th Street-Penn Station to Fulton Street (at William Street).
34th Street at 8th Avenue (Penn Station): the A-C-E (blue line)Take the Downtown A or C from 34th Street-Penn Station to Fulton Street (at Nassau Street).
The A is an express train, while the C is local, but it doesn't make a big difference which one you take. On the A train it's 5 stops from Penn Station to Fulton Street, while it's 7 stops on the C (unless you're traveling late at night, when the A runs local and the C doesn't run at all).
Take the Uptown 1 train (of the 1-2-3, the red line) from 34th Street-Penn Station to 66th Street-Lincoln Center (at Broadway).
Walk 1 block west on 34th Street to Herald Square (the 3-way intersection of Broadway, 34th Street and 6th Avenue).Take the Downtown Q express train (of the N-R-Q, the yellow line), 2 stops, from 34th Street-Herald Square to Canal Street (at Broadway). This is in the heart of Chinatown.You can also take the Downtown N or R local trains from 34th-Herald Square to Canal Street. It's 6 stops.
Take either the Uptown 1 (of the 1-2-3, the red line) or the Uptown C (of the A-C-E, the blue line).You can take the Uptown 1 train from 34th Street-Penn Station to 79th Street (at Broadway).Or you can take the Uptown C train from 34th Street-Penn Station to 81st Street-Natural History Museum (at Central Park West).
You can take the Uptown 1 train (of the 1-2-3, the red line), 2 stops, from 34th Street-Penn Station to 50th Street (at Broadway).Or, you can take the Uptown C or E trains (of the A-C-E, the blue line), 2 stops, from 34th Street-Penn Station to 50th Street (at 8th Avenue).
Take the Downtown A-C-E (the blue line) from 34th Street-Penn Station to West 4th Street. Transfer at West 4th Street to the Downtown F train to Delancey Street-Essex Street. Delancey Street is one block south of Rivington Street.
Yes. Take the Downtown 2 train (of the 1-2-3, the red line) from 34th Street-Penn Station to Flatbush Avenue-Brooklyn College.
Take the Uptown 1-2-3 (the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square. Transfer at Times Square to the R.
Take the Uptown 1-2-3 (the red line) from 34th Street-Penn Station to 42nd Street-Times Square, and transfer there to the N.
Take the Downtown A train (of the A-C-E, the blue line) from 34th Street-Penn Station to the Howard Beach Station in Queens.At the Howard Beach Station, get the AirTrain shuttle (for $5), which will take you inside the JFK terminals.
You can take the Uptown 1 train (of the 1-2-3, the red line) from 34th Street-Penn Station to 50th Street (at 7th Avenue), or the Uptown C or E trains (of the A-C-E, the blue line) from 34th Street-Penn Station to 50th Street (at 8th Avenue).
Columbia University? Take the Uptown 1 train (of the 1-2-3, the red line) from 34th Street-Penn Station (at 7th Avenue, east side of Penn Station) to 116th Street-Columbia University (at Broadway).If the Uptown 2 or 3 express trains come first, then take them and transfer to the Uptown 1 local train at 96th Street. That's 3 stops: 34th Street-Penn Station ---> 42nd Street-Times Square ---> 72nd Street ---> 96th Street. You'll skip 5 local stops.
Take the Downtown 1 train (of the 1-2-3, the red line), 1 stop, from 34th Street-Penn Station to 28th Street (at 7th Avenue).