I am a complete novice, first time gardener, so please bear with me if some of my questions seem ridiculous

Anyway, my wife and I recently moved to Nashville, TN (which I understand is in zone 6B?) and would like to start growing some of our own vegetables this spring. Our new home has a space where a previous resident had a garden; it is approx. 16'x16' and is bordered by what look like railroad ties. Everything I have read up to this point has recommended starting small, so I think this space will work for a first try...
While the garden area isn't covered in actual "sod", it does have a covering of grass, etc. probably 1 1/2" deep. My first question is this: do I need to follow the steps I have read for preparing a new garden I.e. "removing sod" etc., or should I just try to turn this covering under the soil? I have no idea how long it has been since the garden was used; hopefully someone can give me some advice on how to proceed?
We do want to grow these vegetables using organic methods and are looking forward to getting started. Thanks in advance for all advice!!
-JJ