Go down to the housing court in your borough. Take your list of repairs and photos with you to court. Once you get to housing court, tell the clerk that you are there to file an HP action. You will get forms to fill out. Follow the instructions. Be sure to list all of the conditions in your apartment.
It costs $45 to file your case. You will need to pay cash. If you cannot afford the fee, you can ask for a fee waiver.
The judge will look over the documents and sign them. Then, the clerk will schedule you a date and time for inspection by HPD and a date to return to court. You have to serve the papers on NYCHA. Be prepared to go to a post office and pay for postage. You must serve the forms the way the court tells you to. Make sure you understand exactly how you should serve the papers before you leave court.
Before your court date, your apartment will be inspected by HPD. HPD will make a list of the violations in your apartment. This list will go in your court file. The HPD report is proof of the conditions and can help your case.