I also live in an apartment building I have no yard whatsoever but a kind old lady I met on the internets showed me the way. I use a sytem called "grow Buckets" or "Earth Buckets" and homemade carts to move them in and out of the warehouse part of our building. (Local ordinance says I can leave stuff on sidewalk during day as long as people can walk past them easily but sidewalks must be cleared at night)
If you have a balcony or porch that is open to the sun you just need the buckets.
Here is how to make them: DIY Hydro Grow Buckets
BTW I get around 40 lbs (or more) of tomatoes per bucket and the sidewalk they are on is on the west side of the building so I don't get a full days worth of direct sunlight.