I need to get from Hofstra University Law School (in Hempstead NY, on
Long Island) to a friend's place in Williamsburg (Brooklyn) on
Saturday evening.  I don't have a car, but can take a cab/train/subway
-- what are the quickest/least expensive ways to make this trip?

Hello,

The person who made the comment is not quite right. The Hempstead
Branch trains on Saturday evenings do not run directly to Penn
Station. Rather, they run to directly to Brooklyn -- which, of course,
is what you want.

The weekend train schedule for the Hempstead Branch LIRR is at
(http://mta.info/lirr/html/ttn/hws.htm). Ask your friend in Brooklyn
if he or she lives closest to the J or L train (subway). A map (with a
detail of Williamsburg) is available at
(http://www.mta.nyc.ny.us/nyct/maps/submap.htm). To get to the J or L
train, get off the LIRR at East New York. Then take the subway toward
Manhattan to your station in Williamsburg.

It takes 38 minutes for the train to get to East New York and another
10 minutes or so for the subway ride to Williamsburg. See the LIRR
schedule at (http://mta.info/lirr/html/ttn/hws.htm) and the subway
schedule at (http://www.mta.nyc.ny.us/nyct/service/schemain.htm).

The LIRR fare is $5.25 one-way (LIRR fares are available at
http://lirr42.mta.info/index.asp). The subway is $2 one-way.

If you can't find a ride to the Hempstead LIRR station, Long Island
buses 71 and 72 go from the Hofstra campus to the station. A schedule
for that bus is available at
(http://www.mta.nyc.ny.us/libus/pdf/n707172.pdf). The trip is 8
minutes and costs $1.50.

I hope this answer meets your needs. If not please request
clarification.

Search stategy:

New York MTA
://www.google.fr/search?sourceid=navclient&q=New+York+mta

New York subway map
://www.google.fr/search?sourceid=navclient&q=New+York+subway+map

LIRR to the NYC Subway system will be BY FAR the cheapest way to go. 
Take the LIRR to Penn Station, (click here for the schedule
http://lirr42.mta.info/DepartSchedule.asp)
or here for the station homepage with driving directions, and other
info: http://lirr42.mta.info/stationinfo.asp?station=039
Then, at Penn Station, take an A or C train DOWNTOWN/BROOKLYN if your
stop in Brooklyn is on that line.  Otherwise, you can take an A C or E
train uptown to 42nd street, where you can get the N R, W, 2, 3, 9, f,
v, which all run to different parts of Bklyn.
The subway map is here: http://mta.info/nyct/maps/submap.htm.
Will cost ~$10 depending on your time of travel.
Cab/Car Service will cost well over $40.  Will probably also be the
fastest route by far if you're traveling during any hours close to or
between the rush hours (8am-8pm).
Hope this helps