We're told that the way to a weed-free lawn is to cultivate a thick stand of grass. The problem is that most lawn grasses don't grow well in clay soils. Weeds, on the other hand, thrive in clay. A weed-free lawn only exists in lawn product commercials. You can, however, help your lawn grass win the war through good cultural practices -- fertilize, water and amend the soil to make it more hospitable to grass than weeds.
Dig up a handful of soil and squeeze it in your hand. If it forms a heavy, wet ball that holds together, you are strangling your grass with clay.
Use a low nitrogen (10-10-10) fertilizer to treat your lawn grass like garden plants. Weeds don't like fertile locations and they thrive when water is scarce; make sure that your lawn gets an inch of water (including rain) a week. Water only as quickly as your lawn can absorb the water, though --- clay does not hold water as well as soil that contains enough organic matter.
Rent an aerator to improve your soil's "friability" --- its ability to drain water and contain air. Aerators poke holes in the topsoil that allows water, nutrients and air to enter and break up moderate clay soils. The humus that forms in the thatch layer of grass clippings and worm tailings fills the holes.
Distribute 2 inches of humus or peat moss on top of the lawn in the fall. Aerate the lawn in spring to mix the top dressing into the soil. The holes will fill with top dressing and humus.
Add 2 or more inches of compost mixed with an equal measure of humus or well-rotted manure on top of the existing soil to improve existing soil before reseeding a lawn or starting a new one. Work the amendments into the top 4 inches of old soil well before leveling and planting.