What is the best way to start an organic garden?

Great idea! I'm very excited for you to start this one!!

http://www.goodhousekeeping.com/home/gardening/advice/g2104/organic-gardening-tips-460309/

Save all of your kitchen scraps every day and throw them out into the garden, Crushed up eggs shells, potato peels, carrot peels and tops, lettuces leaves, apple cores, cabbage centers and leaves, cucumber, etc, centers of bell peppers, everything but onions and citrus fruits.. I even throw the scraps into the garden area during the winter months as it nourishes the ground and dirt .. The scraps are a natural fertilizer... I till all the scraps into the dirt before planting and then till again after harvest. I even till all of the green grape tomatoes that haven't grown enough to pick before winter sets in and I don't ever have to plant grape tomatoes or bell peppers as they just come up by themselves every spring.. I get the largest grape tomatoes plants every year that have huge clusters of grapes.

I also put lawn clippings and shredded leaves as mulch on top of the soil and till into the soil the next spring. By the time it is tilled into the soil the next spring I already have a couple of inches of degraded mulch to till in.