i was going to post something similar to farmwithjunk. in doing my readings, i have run across many articles about how over-tilling is bad. this mostly has to do with destroying capilarity and micropores in the soil. the only time you need a really fine seedbed is for very small seeds that can't physically push up through larger clumps of dirt. (lettuce, carrots, etc.) most larger seeds will actually do better in a moderately rough seed bed. larger chunks provide slower and longer release of soil nutriets, allow water to penetrate more deeply, and perhaps most important of all, will allow oxygen to get down to the roots after that first big rain forms the hard crust farmwithjunk mentions.
all of these problems are significantly lessened if you have a nicey loamy soil to start with (rare). if you're like most of us, you have either too much clay/silt or too much sand/rock. the first option gives you the hard crust, the second option gives you drainage and fertility issues.
unless you are blessed with a fertile loam, unfortunately, you should have started soil renovation for this year's garden last year. then you could have done your subsoiling, tilling and sod busting/destruction operations last year, added amendments, and given it the winter to stabilize and settle. then a little spring cultivating and you would have been ready to plant.
but, that opportunity is gone now. your only choice to destroy the sod is to pulverize it beyond recognition or use chemicals. we hope you don't have bermuda in your grass, or it will most likely be a problem for you all year as it can come back from very tiny pieces of rhizome.
i would do the best i can this year and plant lots of green manure crops and a few hardy vegetables and then this fall, do a proper prep. you could also put in some raised beds, focus on soil amendment and focus on fencing the area if deer or other animal pests are a problem in your area.
things will be much easier for you next year.
good luck!
