The MTA is planning to restore partial subway service tomorrow, November 1st, in addition to the already restored local bus services (which are understandably crowded).
Everything isn't back to normal yet though, especially if you are in Brooklyn, south Queens, or lower Manhattan, as there are no Brooklyn <> Manhattan trains, and no trains in Manhattan south of 34th Street. MTA is also running shuttle buses between downtown Brooklyn and midtown Manhattan.
The MTA released the following PDF map showing which lines, or partial lines, are active.