A criminal record does not prohibit you from obtaining a passport, unless travel outside the United States is prohibited as a condition of your sentencing, probation, or parole.  You will need to have several basic identity documents in hand to make an application.  Full guidance is available here at this US Department of State site.  Know that once you have completed your application, collected your documents and obtained a photo, you can submit your application at an approved site, which includes several Westchester County libraries as well as US Postal Service offices.