Worms -- lots and lots o' worms -- organic material, and time.

There are a few different species of worms that will work well for you,
including the good ole fashioned nightcrawler. Red wigglers (eisenia
fetida) will be good for the upper 12 inches or so and breaking organic
material down. The other worms will work their way down and carry good soil
with them, plus their tunnels aerate of course. With attention and lots of
organic material, you can transform a good chunk of the clay (pardon the
pun) into good soil.

As for seeding your grass, give the manure some time to settle in before
seeding and it will be fine. You can add topsoil and till as well. (For
that matter, I'd start raiding the neighbors leaf bags on trash day -- lots
of good organic material in there and it will do wonders for your soil.)

One question comes to mind -- did you basically just spread the manure over
clay or was their some measure of topsoil there?