To get from Philadelphia to New York City, you can take the train, the bus, or drive. You could also take a taxi, but it would be very, very expensive.
The train that runs to NYC is the Amtrak, which you can board at 30th Street Station. Several buses go to NYC, including the discounted Megabus and Bolt Bus. Driving to NYC is also an option.
In terms of affordability, taking the bus is the cheapest option. Next would probably be the train, since if you drive to NYC, you also have to account for the tolls (which I think are, at minimum, $13) and parking costs once you get to the city (which could be around $25) in addition to gas.
