You may have to take several approaches. To start, read up on Corn Gluten Meal
and Crabgrass Killer
. Spot spray weeds (or general application in winter when grass is dormant and weeds are out) with Vinegar Weed Killer
Poke around in Howard's Natural Organic Library
for tons of more answers.
As one of those folks with a weedy lawn, I try to do my neighbors a favor by keeping it mowed so the weeds don't go to seed, but I have so many other things to do with my time and money than hunt down weeds. If you've ever seen the old one-panel "Pluggers" cartoon, you may have seen the one I clipped years ago with the caption "Pluggers know that mowed weeds look just like turf."