You can't get one in New York. A friend of mine accumulated the 6 points needed (brought along the SSN ineligibility letter) and they asked him to prove he was here legally. After he did, he got a temporary NY State ID which expires on the day his visa expires. So, there really is no way to get one in NY if you are undocumented.

However, I know that in Washington (this one is definitely possible), Oregon, New Mexico, Utah, Hawaii and some other states you could obtain a DL. Granted, you have to have certain paperwork, but it is doable.