Add lots and lots of organic material, compost, mulched leaves and the like. Some organic fertilizer to get things going may not be all that bad either.
I had the same problem with lack of topsoil and found that adding the organic material will allow worms to come in on their own and start taking up residence. You may also want to incorporate Paul's worm pits. I did that too and it seemed better than aerating. The key is to get the soil to hold moisture and only organic material can do that well
enough to establish a soil that is capable of supporting microbial and offer forms of life. Your soil has to be alive for it to work as intended. It will then feed the grass and lower the incidence of weeds. Clover should not be considered a weed as it brings nitrogen to your soil from the air.
This whole process may take a few years to get going, but it will be worth it. I did enough last year that I did not add anything this year. Only mulched the grass on the lawn. Another important point is to mow high. At least three inches, and more if you can. I leave the mower set at its highest setting, about three and a half inches for the season, then cut it short for the winter.
Since it is fall here, I am going to mulch the fallen leaves and maybe add a little compost. Do the last mow at about an inch and a half, and then leave it till spring. If it comes up like it did this year, I will be happy.
Good luck to you.