Do they help with finding own apartment?

Yes they help you but that don't mean they going to do all the work for you they show you everything you need you have to do some work yourself too

Yes they do help. First you will be put in an emergency shelter for 10 days while they approve you for a more permanent shelter. In the emergency shelter you'll get a social worker that will ask what income you have, if you don't have income it's ok they still will help you. They'll ask you like where what city do you want to live in. Then they will give you options to choose from Section 8, city pheps, & other programs.

You gotta do the work yourself unless you get a good worker other then that bare minimum

It's a process to get an apartment. U must be living in the shelter for 90 days. Then u become eligible for a voucher. Unless u can afford nyc rent on your own.