Question
That should be 15-20 YARDS of topsoil over the clay.  This is just a recent problem.  Sorry for the typo!
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Followup To

Question -
"If you have the best topsoil in the world delivered -- and it will never be as good as the stuff you can make yourself -- the topsoil will be sitting on top of an impenetrable layer of clay. Which will flood every time there's a thunderstorm."

This previous answer of yours perfectly describes my problem.  We had a brick patio installed in our back yard last month.  The tractor delivering the bricks made deep ruts in our lawn all the way from the street.  The area was filled with 15-20 yrs of topsoil over our clay soil (SE Michigan).  We're trying to grow grass again, but a lot of this area never dries out.  My husband walked across it the other day (3 days after rain) & went into the muck over his ankles!  Can we add anything to the loose soil to harden it or rototill it into the base clay?  Help!  We want our lawn back!  Thanks!

Answer -
Jan - you have lived with this problem for 20 years?

Yikes!

Let me speak to a few people and see what they think.  I have some thoughts to run by them.  

Rototilling is a very delicate matter.  If you do it wrong, you make it worse.  

At the same time, if you are using chemicals on your lawn, you halt the development of the soil and create limits on what you can do.  

This is fortunately the perfect time of year to deal with this problem, inasmuch as you aren't going to plant any grass before September (if I have any say about it, that is).

You can have a really beautiful lawn next spring.  Which would be nice since you have that new patio to admire it from.  Give me a day or two and let me see what answers I can come up with for you.

Answer
The problem here is that if you have clay that actually is not able to dry out - do you get that much rain? - it would be suicide to Rototill.

Clay pulverized with topsoil under wet conditions turns into natural cement - the entire soil structure is totally destroyed, and it takes years to recover.  It would be worse than what you have now.  Practically moondust.

So tell me, does that land dry out?

If it actually does get dry - it does not have to be bone dry, just reasonably dry, enough that you would have particles as opposed to a cement-like gooey mix - you would be doing yourself a favor if you Rototilled nice and deep your "topsoil" and the clay bed with amendments to build a rich, healthy layer of good earth to grow your grass.

No secret formulas here.  The usual humus and compost, even some peat moss, would be perfect.  Rototill just enough to mix.  If you were baking a cake, it would be "just to mix the ingredients, do not over-mix".  Same deal.  Or you will obliterate all chances of achieving a good, granular soil structure with "good tilth".  NASA has a soil science education page (soil.gsfc.nasa.gov/pvg/prop1.htm) that simplifies the whole routine.  Roots grow well in soil with good tilth and not at all in bad tilth soil.  DO NOT OVERMIX!

If you add some granulated lime while you're tilling, in a few weeks you can take a soil sample for analysis and see what your new dirt is made of.  They will break the sample into the good, the bad, the ugly - everything you need to know to grow beautiful grass.  

An amendment of peat might help to absorb some of the excess moisture if your clay bed reaches way down.  

Grading for a downhill slope, toward the edge of the property, will keep water from sitting in a single location.  

Perhaps a drainage system would help in an extreme case.  

Not being there, it is hard to see how serious your moisture problem is.  Those are your options.

Don't plant grass early.  This is the time to fix the soil.  Grass seed is best planted in the early fall.  Since you're going to all this trouble, get yourself a first rate grass, either locally or at Seedland (www.seedland.com), which has a lot of advice and hundreds of selections.  You can't get a first rate lawn w/o first rate grass.

I must say I am relieved that you have not waited 20 years to address this.  If your property is the kind that NEVER dries out, other measures beyond Rototill must be sought.  Please advise if that's the case.  Good to hear from you.