Thedawnof31 is mistaken, there are numerous Long Island Rail Raod stations in New York City, including the main Long Island Rail Road station, which is in Jamaica in Queens -- the largest of the 5 boroughs of New York City. I think what Thedawnof31 meant to say was "the LIRR station in MANHATTAN is Penn Station", which would make the statement correct.
As noted, Penn Station is the Manhattan terminus of the LIRR. It is very easy to go form the New Jesey transit trains in Penn Station to the LIRR, and that is what your friend should do. The question then becomes which LIRR station on Long Island (and note that both Brooklyn and Queens are on Long Island; most people who live on Long Island actually live in New York City, and msot New York City residents live on Long Island!) your friend should go to to meet you.
The closest LIRR stations to LGA are Flushing Main Street on the Port Washington Line, and Woodside on the Main Line. As all trains that stop at Flushing Main Street stop at Woodside, and as other trains stop there as well, Woodside seems a good choice to me.
Edited: 18 July 2012, 7:57