Public HS Admissions Calendar on the DOE website can be accessed through the following link (hopefully it is actually a link otherwise copy and paste). It will give you information about HS Admissions sessions, etc. If you cannot copy & paste, then type what you see as the URL and it will get you to the current HS Admissions calendar.
The Public High School Directory is also on line. The fastest way to get to it is to google it. The link will be clearly stated. The public high school admissions office has also put a Search section on their site, so that you can find your zoned high school, schools with interest areas, locations, etc.
Important: please read through the Introduction in the High School Directory. It clearly gives you their admissions process. You can also go to their information sessions to ask them questions directly, and get a Directory and the Specialized HS/LaGuardia Student Handbook.