I just took a job in nyc. What taxes am I responsible to pay, New York state, nyc , both or just one?

Depends where you live. NY City tax is only paid by residents of NY City. So if you live in NYC, then you pay NY State and NY City income taxes. If you live in NY state but outside of NYC, then just NY State income tax. If you live out of state, then you pay NY State non-resident tax plus whatever you might owe to your home state. Your home state lets you deduct taxes you paid to NY State, so in many cases your home state tax liability is quite small.

ebaines:

A slight correction. It is not a deduction on your home state tax return for taxes paid to NY, it is normally a credit, often dollar-for-dollar.

I know most of my clients who live in NJ and work in NY pay JUST NY state taxes, because the resulting credit completely offsets the NJ tax liability.