There are no subways or train lines close to LaGuardia airport. There are buses. There is a bus called M60 SBS that you could take to the 125th Street Station of Metro North. From there it is a quick easy trip to Fordham, as I've explained elsewhere. (Do not confuse that station with one of the subway lines.)
Your best option may be to take a cab or car service. These will probably cross the Whitestone Bridge, one of the least likely bridges in the area to have bad traffic jams.
Proceed to the "Ground Transportation" area. Do not accept offers of transportation from anyone while getting to the ground transportation station. There, the official dispatcher will direct you to legal and safe transportation services. The dispatcher will inform you what your charge would be.
By inquiring at the Ground Services Information Booth at the airport you can arrange for door-to-door car service. To learn more about different door-to-door services go to Port Authority's website http://www.panynj.gov/airports/lga-taxi-car-van-service.html.
Also look at this: http://www.nysubway.com/airport/laguardia.html
Make sure you tell them you want Fordham University ** IN THE BRONX. ** It's next to the Bronx Zoo. If they don't know what that means, get another taxi.