Learn the pattern of where the subway stops at the station. The drivers still have to follow protocol when it comes to stopping trains at a particular station. This means the doors will open in the same spot most of the time. Figure out where those spots are and go to them when you arrive at the platform.
Stand just to the side of where the doors will open. When people get off the subway, they come straight out. By standing on the side, you'll have a clearer path to the entrance of the train when the doors open.
Allow passengers to exit the train once the subway has stopped. This is common courtesy as well as an unwritten rule amongst New Yorkers. Also by allowing people to exit, you are creating the space for which you can get on the subway.
Place your foot inside the train as soon as you have a chance. Again rather than walking straight in, shimmy yourself on the side. This will allow you to inhabit a space that people aren't naturally prone to consume. Once you have a foot in, you are home free, as nobody will push you back out.
