Can anyone tell me how to get first month's rent help in New York city

You can try HUD, Salvation Army, Catholic Charities.
If they can't help you they should be able to refer you to places that can help. Many places require that you do have a steady income for them to help.
Here is a search engine of places and info
rent assistance n y c - Google Search (http://www.google.com/search?hl=en&client=firefox-a&channel=s&rls=org.mozilla%3Aen-US%3Aofficial&hs=qpz&q=rent+assistance+n+y+c&btnG=Search)

If you are low income have you applied for government assistance in housing