I live at the north tip of Staten Island, near the Staten Island Ferry Terminal and up the hill, in The Wisteria, 141 St Marks Place, a 1929 building in historic St. George.
B: Walking or biking, subway, ferry, and bus
C: From the Ferry Terminal in Staten Island
D: From Richmond Terrace near the Ferry Terminal
E: From St Marks Place at Hamilton Avenue
Presently (while the ferry terminals at both ends are being reconstructed) you cannot take cars or motorcycles on the Staten Island Ferry.
You can take unmotorized bicycles on all ferries. In this case go to B.
Else find the Staten Island Expressway, also known as I-278, from New Jersey on the east or Brooklyn on the west. In either case, take the Staten Island exit nearest to the Verrazano Bridge, Bay Street.
If coming from Brooklyn, follow the exit ramp onto the street, then continue for 2 blocks to a T-junction and traffic light. If coming from New Jersey, turn left at the light at the end of the exit loop, go under the freeway, then continue for 2 blocks to a T-junction and traffic light.
In either case, turn left here onto Bay Street.
On Bay Street you are going around Staten Island anti-clockwise, e.g., the water is on your right.
Follow Bay Street for 2.7 miles from the T-junction (2.8 miles from the exit from the Expressway) to where it heads you directly into the Ferry Terminal. It looks like this:
Immediately before entering the Ferry Terminal, turn left at a traffic light, and you are on the continuation of Bay Street, which is Richmond Terrace.
Find the taxi-stand for yellow New York City taxis. When you get to the head of the line, tell the dispatcher that you are going to Staten Island.
You will pay what is on the meter plus the toll plus a tip. The toll is $10 for crossing the Verrazano Brige (only one way). The tip should be about 20% of the fare (if you are satisfied). The total could be $100.
If the driver does not know the way, say Cross the Verrazano Bridge and then I'll guide you.
Inside your terminal look for the AirTrain sign. This is a driverless elevated train.

Take the Howard Beach train to its terminal at Howard Beach. No charge to board the AirTrain.
When you reach Howard Beach, walk out to the AirTrain lobby. This area is fenced by turnstiles, and features red-coated helpers and Metrocard machines.
Use U.S. cash or a credit card to buy a Pay-Per-Ride (Regular) MetroCard for at least $7. You will need $5 to pay for the AirTrain and $2 to pay for a subway ride and bus.
Buy a Metrocard for more money if you want extra rides on the subway and the buses while you are in town. Ask for help if you need it. Ask for a subway map.

Swipe your Metrocard at the turnstiles on the left toward the Manhattan A train.
Go down to the platform by the elevator or the escalator, and take the first train (A) that comes. The train runs an elevated route and then a long subway route.
Get off the train at Broadway-Nassau St.

At Broadway-Nassau St walk toward the front of the train and take the steps up marked Downtown & Brooklyn 4 5 transfer.
Follow the corridor and go up the steps to the Fulton St platform. Take the first train (4 or 5) that comes, two stops to Bowling Green.

At Bowling Green walk toward the front of the train and take the steps up marked Exit Battery Park. State St & ferries to Liberty, Ellis & Staten Island.
Walk forward to the left of the fence. Disregard the rightward arrow which points to the wrong ferry.

Walk two blocks toward the blue STATEN ISLAND FERRY sign.
Enter the ferry terminal. Use the escalator or elevator. Take the ferry. See B.
Note on bicycles: You can take unmotorized bicycles on the subway and the ferry, but not on the bus.
Find the Staten Island Ferry Terminal at the southern tip of Manhattan (South Ferry or Battery Park).
The 1 subway to South Ferry (the Ferry Terminal is upstairs)
The R or W subway to Whitehall St South Ferry (the Ferry Terminal is across the street)
The 4 or 5 subway to Bowling Green (the Ferry Terminal is two blocks south via State Street)
Take the M1, M6, or M15 bus to the last stop at South Ferry. The Ferry Terminal is within a block of the last stop - the actual last stop is being moved around during the reconstruction of the ferry terminal. (Warning: The M1 does not stop here on weekends and holidays.)
Or take the the M9 bus to South Ferry (not quite the last stop).
For any of these, buy a Metrocard at any subway station or some newsstands.
The ferry schedule is at http://www.nyc.gov/html/dot/downloads/pdf/siferrysched07.pdf, or call the City of New York, within New York City call 311, or outside New York City call +1-212-639-9675.
In general the ferry runs twice an hour, on the hour and the half hour; in rush hours more often; late nights and weekend evenings once an hour on the half hour.
The ferry crossing takes about 20 minutes. Admire the view.
On the Staten Island side, this is where you want to get to (left red arrow) via the S42 bus (right red arrow)
At the Ferry Terminal on the Staten Island side, get off on the upper deck, and follow the crowd.
You will walk either left or right around the central waiting room, and then find yourself in a long hall with stairs down to trains and ramps up to buses:

Along one side of this hall are ramps sloping up. These lead to bus platforms. Find Bus Ramp C, leading to the S42 bus.
Climb the ramp and walk to the end of Bus Platform C.
By bus? Wait for the S42 bus at the end of the Bus Platform. Take it when it comes. The S42 meets every ferry except between 2 a.m. and 6 a.m. Pay with your Metrocard (the transfer will be free if you already took a subway or bus on the other side).
Counting the Ferry terminal as the first stop, get off at the 8th stop, at the corner of St Marks Place and Nicholas Street. The bus stops in front of my door.
Beware!
Another way to find the right stop:
The bus first winds around many corners to the top of the hill, then runs along St Marks Place. After 3 blocks, it passes two 20-storey Castleton Tower apartment buildings on the right. Get off at the next stop.
For a picture of the Castleton Tower apartment buildings, go to E.
You are on Richmond Terrace near the Ferry Terminal, with the harbor on your right.
Take the third left, second traffic light, past the police precinct on the left and the ballpark on the right, Hamilton Avenue.
Walk to the top of the hill (3 blocks) to the stop sign.
This is St Marks Place. Turn right.
Go one block past two 20-storey Castleton Tower apartment buildings on the right. My building is the smaller building beyond them.
Continue to the intersection of St Marks Place and Nicholas Street.
My building is the old 5-storey apartment building on the right.
I am in 5-F (fifth floor).
Nicholas Zvegintzov
141 Saint Marks Place, Suite 5F
Staten Island NY 10301 USA
telephone +1-718-981-7842
mailto: zvegint@hotmail.com
http://www.maint.com