Answer:
It depends on where on 33rd Street you're coming from and where on Varick Street you're going to.
From West 33rd Street, you can take the Downtown 1 train (of the 1-2-3, the red line) or the 2 late nights, from 34th Street-Penn Station (at 7th Avenue) to Houston Street, Canal Street or Franklin Street. All three of these stations are on Varick Street.
From East 33rd Street, you can take the Downtown 6 train (of the 4-5-6, the dark green line) from 33rd Street (at Park Avenue South) to 14th Street-Union Square.
Transfer at 14th Street-Union Square to the Manhattan-bound L train (the grey line), one stop, to 6th Avenue-14th Street.
Walk through the tunnel that connects the 6th Avenue-14th Street Station to the 7th Avenue-14th Street Station. At 7th Avenue-14th Street, get the Downtown 1 to Houston Street, Canal Street or Franklin Street.