Tining it to aerate it, dusting organic manure compost on it, watering it compost tea, leaving grass clippings on it for mulch once in awhile, don't mow it too short so it won't eat up the nutrients trying to grow back.

Compost, spread about 1/4 inch thick, on top of the lawn about once a month during the growing season will work. Perhaps this episode of Growing a Greener World where Paul Tukey outlines organic lawn care might be of some interest.

Here is a link that might be useful: organic lawn care

This post was edited by kimmsr on Mon, Mar 10, 14 at 6:29

Or get rid of it! I can't tell where you are, but here in sunny drought ridden CA lawns aren't a good thing!
There are some forums on drought gardening here and other ideas. If you're in a place with plenty of water, there are also forums to peruse. Nancy

Soil is made of the mineral portion, the sand silt, or clay particles, and organic matter. If someone lives where the primary mineral is clay getting rid of that soil will be nigh onto impossible.

I think nancyjane was referring to getting rid of the the grass, not the soil.