If you're unsure what goes in each bin, here's a guide straight from the source, the NYC Guide to Clean & Green Schools.
According to the guide, if students/staff properly recycle, then the various forms of waste go to the following places: Clean paper & cardboard go to local paper recycling facilities, or directly to a paper mill on Staten Island. Metal, glass, hard plastic, and cartons go to local materials recovery facilities that resell the repurposed materials.Food scraps & food-soiled paper go to regional facilities to create compost (a fertilizer for soil) or to create renewable energy.