The first thing I did was accept that a "perfect" lawn was not necessary. Perfect is in the eye of the beholder. I pulled dandelions daily in the spring with a tool that looks like the one on the left in this article. Sorry, I no longer have a house or the tool, so I can't look up the name. http://www.pesticide.org/dandelions.html
Dandelions are tap rooted perennials, so you must get the entire root. They also produce massive quantities of viable seeds, so I'd go out daily and find everything that was blooming and pull it, much easier to do when the lovely yellow blossoms are shouting "here I am"! This article I found is pretty cool. http://www.pesticide.org/dandelions.html
Once you are sure that there are no chemicals in your lawn, you can eat the dandelions. Of course, drift from the neighbors is a concern. Some fun information. http://www.wildmanstevebrill.com/Plants ... elion.html
Cutting the lawn high, 3" or so, with a mulching mower is definitely the right way to go. The longer grass shades the plants, decreasing the water loss. It also shades out non-desirable plants. A notable exception to this is crabgrass, an annual that also produces massive quantities of viable seeds. Crabgrass has the annoying capacity to grow low and well. That's another one I policed the lawn for by hand. Oh, and it likes your flower and garden beds as well. I didn't like the pre-emergent chemicals, but a neighbor who chose an organic lawn used a corn gluten product with very satisfactory results. He is a golfer and needs a perfect lawn. Snicker, my violet laden one must've driven him nuts. He also used a product called milorganite, if I remember correctly. Stinks to high heaven, but man, his lawn is a beauty. They did not want their dog playing in the lawn chemistry, and although it stinks, it didn't harm the dog. A comment on the pre-emergents treatments for crabgrass, I do believe that it also inhibits the germination of grass seed. Man, my turfgrass class was a long time ago.
Make sure you have the right grass variety or mix for your local conditions. Your local extension service can help with that information.
If your soil has a great deal of clay in it, trying to significantly alter the pH is an exercise in futility, as clay has an amazing buffering capacity. Again, ask the extension agent.