It really depends on where you live.According to the DOE if you live in districts 1,3, 25 or 29 you have the opportunity to rank your choices for kindergarten admissions on an application.
If you don't live in those districts, but live in a zone with a very crowded school, you might want to look into alternative schools and apply to those as well. You would apply directly at each school. MOST schools in the city do have room for all kindergartners who want to attend. In a few cases schools have had to cap the kindergarten and send the children elsewhere.
Where do you live?