From Newark Airport:
Take the AirTrain from your airport terminal to Newark Liberty Airport Station
Take an NJ Transit train from Newark airport to New York Penn Station
Exit via 8th Avenue & 33rd St. at SE cornet and head northeast. Walk about 5 minutes on 8 Avenue until you are in 545 8th Ave. (& 37th Street)
From JFK Airport:
Take the AirTrain from your airport terminal to Jamaica Station
Take a Long Island Rail Road from Jamaica to New York Penn Station
Exit via 8th Avenue & 33rd St. at SE cornet and head northeast. Walk about 5 minutes on 8 Avenue until you are in 545 8th Ave. (& 37th Street)
From La Guardia Airport:
Take the Bus Q70 SBS LaGuardia Link from your airport terminal to Woodside station at 61 St/Roosevelt Av
Take a Long Island Rail Road from Woodside to New York Penn Station
Exit via 8th Avenue & 33rd St. at SE cornet and head northeast. Walk about 5 minutes on 8 Avenue until you are in 545 8th Ave. (& 37th Street)
Other Options:
Lyft and Uber apps also connect riders with drivers within minutes, so you could call a cab once you've got your luggage from the carousel.
Private cars and taxis are likely more expensive than ridesharing apps, and you should familiarize yourself with the TLC Fare Guide and the Taxi Rider's Bill of Rights if you plan to use the former options.
Additionally, several companies offer private shuttle services to and from Manhattan. Go Airlink NYC offers shared transfers from LGA 24 hours a day while NYC Airporter is the official bus service of the NYC area's three airports. With NYC Airporter, you can access service between Grand Central, Port Authority or Penn Station and LGA, JFK, and Newark Airports.
Super Shuttle is another great option, especially since you don't need to book reservations in advance to take the Super Shuttle from the airport. However, you can book a reservation online and the super shuttle will pick you up anywhere in New York City and take you to LaGuardia for a flat fee.