Can someone explain to me how exactly to get access to the NY State Census records for New York County?

As is my understanding, the 1905 census is the only one available online. But what if you want to view the other ones? I know a lot of them were destroyed in a fire, and at least the 1855, 1915, and 1925 survive somewhere.

So what's available to view, and where can I view them? The New York County Clerk's office had no information on this. Do I have to go to Albany? And am I able to search by name? My family moved around a lot and I doubt I'll be able to find them in the same places as the federal census.

Any info would be appreciated!