Go to the bus station at the airport. There is a separate bus station for every terminal, indicated as ground transportation. For terminal A, it is to the side of the terminal, the right side if you look onto the road. For B and C, it is in front of the terminal.
Do not take the bus labeled "Newark Airport Express" to New York Penn Station. It is slow and expensive.
Instead, take New Jersey Transit bus number 62 from the bus station to the final stop, Newark Penn Station. Cost: $1.25 Time: 20 minutes
Enter the station. Go to your left in the hallway to "Track 1, Path" and as you see track on turn arround to face the entrance of the PATH train. Pay take the PATH train to the last stop, 33rd Street. Some trains go to the World Trade Center. When you are on such a train change at Journal Square for a train to 33rd Steet. Cost: $1.5 Time: 40 minutes
Change into the F train of NY subway to Roosevelt Avenue/Jackson Heights. Cost: $2.5 Time: 30 minutes
Take the airtrain to Newark International Station, and change into a NJ Transit train to New York Penn Station Cost: $14 Time: 30 minutes
Change into the E train of NY subway to Roosevelt Avenue/Jackson Heights. Cost: $2.25 Time: 30 minutes