You can apply for a sabbatical by logging onto the DOE's Self Online Leave Application System (SOLAS). SOLAS is available at https://apps.schools.nyc/solas.
If you are a teacher with 7 years of service, you could be eligible for a six-month sabbatical. People on six-month sabbaticals are paid 60% of their regular pay. People who are on year-long sabbaticals (which require 14 years of service) receive 70% of their regular pay.
See the UFT's main page on sabbaticals for more information.