Buy a Pay-Per-Ride Metro Card for 5 dollars before you leave the terminal. This card will allow you to transfer from the bus line to the subway line for free once you are in Manhattan.
Note that if you don't buy the Pay-Per-Ride Metro Card at LaGuardia you can pay in exact change when you get on the bus. Just be sure to ask the bus driver for a transfer when you pay.
Look for the M60 bus line outside the terminal at LaGuardia. Check the posted schedules for times. This route runs between 5 a.m. and 1 a.m. and stops outside of every terminal at LaGuardia.
The M60 will take you directly into Harlem and make many stops before terminating at 106th Street and Broadway. All stops are within walking distance of subway lines and the connecting North-South bus lines. If you need to transfer to the Metro-North train station (which isn't the subway but a commuter train that goes into Connecticut) you can do that at the 125th Street station.
