At MTA.info the Metropolitan Transportation Authorities are working hard to restore their services. For quite a few residents in New York the transit and metros are their only means of transportation from place to place other than taxis - so having a lack of public transportation has really become something detrimental for those in the area.
The site says:
The MTA is working hard to restore service in the aftermath of a storm that dumped more than a foot of snow in parts of the region. Service is suspended in parts of the system as crews continue to remove snow and ice from tracks, switches, stations and roadways. Please check back to MTA.info for the latest updates, allow extra time and be careful when walking and boarding.
The site then lists specifics for each transit including New York City Transit, MTA Bus, Long Island Railroad, Long Island Bus, Metro-North Railroad, and others.
CBS gave an update that many of the services have been restored, but to keep checking on the actual site for more information that is up-to-date.