Many people ask about simple wasy to compost when you don't have a yard space. There are options for us yard-less folks. I started a small worm composting bin when I lived in a small apartment. You can learn more about worm composting here. I have curbside composting in our city which means I don't have to worry about it at all.
I wanted to share an option that was presented to me for those who would like an easy verison of dealing with food scapes without taking up much space at all. Bokashi is a Japanese term meaning 'fermented organic matter'. And it may be just the solution you're looking for! I'm linking a great article by The Compost Guy on bokashi in the buttom below!