How could I get back to the US?

First, in New York (and in every other state), jumping a turnstile is a theft of services. In immigration law, all thefts are considered crimes of moral turpitude (meaning they show that the person who committed such crime is not a moral, honest person). Conviction for a crime of moral turpitude made you inadmissible (meaning that you are not eligible for any visa or a green card), but you can apply for a waiver of inadmissibility. Second, since you were deported (which should not have happened if you had a competent attorney), you now cannot come back for 10 years. However, again, there is a procedure for asking permission to re-enter the U.S. sooner. Third, you need some status in which you could come back. It is not likely that the government would give you the waivers so you could come to the U.S. as a tourist. Getting a student visa might be not completely out of question, but I would not recommend spending time and money on chasing this dream. Better chances could be associated with a petition of a U.S. or international business requiring your services in the U.S. as their executive or specialist, either on a work visa or on a green card. Finally, your best chance to obtain waivers is tied with an immigrant visa petition of your U.S. spouse, parent, or son/daughter.