You can use this form to suggest uses that the community wants to see as concessions in a NYC Parks building. NYC Parks will consider your fantastic ideas but keep in mind that NYC Parks isn't going to do your project for you.
Opening buildings and renovating parks costs money but NYC Parks has a limited budget. Here is a great guide to how to get money for your NYC Parks building stewardship project, created by the Center for Urban Pedagogy, New Yorkers for Parks and Partnerships for Parks. Follow the tips for "Capital Projects."
Getting your Council Member and Borough President on board is key: both have money to give out every year via their discretionary budget; some Members allocate some of their discretionary money to Participatory Budgeting. You can get involved to get the word out about the need to re-activate the building or park you want to steward.
A building or a whole park could be landmarked. If it is, any work will need to comply with these rules.
CityParks Foundation and NYC Parks' Partnerships for Parks program can help you figure out what other steps to take. In their own words: "Partnerships for Parks is the public-private program that supports and champions a growing network of leaders caring and advocating for neighborhood parks and green spaces." They have helped dozens of groups of people just like you take care of NYC Parks and buildings in them. Start by finding your outreach coordinator here.