The backyard garden is in vogue right now. If you'd like to grow a few veggies yourself but your backyard soil isn't conducive to keep anything other than crabgrass alive you can start your urban homesteading efforts with a bag garden. This will give you immediate results now and help build your soil for next year.
Homesteading magazine Mother Earth News offers a great way to establish a garden in an area with poor soil. Buy bags of potting soil and cut open the top side, leaving enough plastic on the sides to keep the bag together. You can plant many types of seeds directly in the 8-9cm of potting soil and most will have plenty of room to grow to maturity, but I'd avoid carrots. Lettuces, spinach and radishes will do very well.
If you place your garden beds in the area where you'd eventually like to have a permanent garden you'll build good soil by mixing the original potting soil with compost.