The same way they move in and out of every city. Shipping rigs float in and out of the seaports around Manhattan, trains move freight over tracks, trucks carry goods in and out of the city through tunnels and major bridges, and cargo planes operate from every major airport. Commercial shipping companies, like FedEx, DHL, etc, operate primarily with motor vehicles and planes, with large-scale water transport reserved for bulk and oversize cargo headed to/from wholesale points. Everyone moving goods in and out of New York City has to interface with the Port Authority:
"The Port of New York/New Jersey is the largest port complex on the East Coast of North America and is located at the hub of the most concentrated and affluent consumer market in the world, with immediate access to the most extensive interstate highway and rail networks in the region. In addition, The Port Authority directly oversees the operation of seven cargo terminals in the New York-New Jersey region. Each terminal offers comprehensive shipping services, a qualified, highly productive labor force and competitive pricing. The Port also provides a fast and efficient rail and trucking services. Our SEA LINK® Driver Identification Program speeds cargo processing. The Port Authority of New York & New Jersey is a bi-state agency formed in 1921 to promote trade and commerce in the entire port region and has been the grantee for FTZ No. 49 since 1979."