Working remotely from Texas for a job based in New York City

I will be starting soon at a job based out of New York City but will be working remotely from home in Texas. I was just wondering what I can expect my employer to be withholding from the paychecks I will receive and what I will actually have to pay in the end? Texas itself doesn't have a state income tax, but New York state does and so does New York City. So I was just wondering what I will have to pay in the end? Also, how will I go about filing taxes? Will filing be different from when you and your employer are in the same state?