How much water depends on many things, starting with what kind of soil you have. As a general rule, when all conditions are close to perfect, a lawn needs about 1 inch of water per week, but temperatures, wind, and sun can affect that along with how much organic matter (aids in holding moisture) is in the soil. Recent research has been showing that deep once a week watering is better for a lawn then shallow every day sprinkling, such as is done by the automated irrigation systems.
Most soils I have seen in Indiana are clay, some near Lake Michigan have been sand, however, and clay soils need lots of organic matter mixed in to allow plant roots to access the moisture and nutrients held in that clay.
You may want to use these simple soil tests to see where your soil is
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

The current issue of Organic Gardening magazine, August/September 2012 has an article that outlines a similar test for organic matter in soils.

Scroll to the bottom for organic lawn FAQs.

It's a little tricky. The FAQ link is in Organic Gardening instead of the Organic Lawn forum.

Here is a link that might be useful: FAQs

I use Dr. Earth and find it works great. But it's a slow release fertilizer. You can't expect results in a week.

I don't core aerate at all. If you're doing well with organic lawn care and have a healthy soil food web, you'll get lots of aeration from worms and other critters. What do you think aerates the soil in nature?

kimmsr has left out the easiest change to make: mow high.

Basics of Lawn Care

After reading numerous books and magazines on lawn care, caring for lawns at seven houses in my life, and reading numerous forums where real people write in to discuss
their successes and failures, I have decided to side with the real people and dispense with the book and magazine authors. I don't know what star their planet
rotates around but it's not mine. With that in mind, here is the collected wisdom of the Internet savvy homeowners and lawn care professionals summarized in a few words. If you follow the advice here you will have conquered at least 50% of all lawn problems. Once you have these three elements mastered, then you can worry about
weeds (if you have any), dog spots, and striping your lawn. But if you are not doing these three things, they will be the first three things suggested for you to correct.

Watering
Water deeply and infrequently. Deeply means at least an inch in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly
during the hottest part of summer. Do not spread this out and water for 10 minutes every day. If your grass looks dry before the month/week is up, water longer next
time. If that does not work, then you might have to water more than once per week during the summer's hottest period. Deep watering grows deep, drought resistant
roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.

You will have to learn to judge when to water your own lawn. If you live in El Paso your watering will be different than if you live in Vermont. Adjust your watering to your type of grass, temperature, humidity, wind, and soil type. It is worth noting that this technique is used successfully by professionals in Phoenix, so...just
sayin.' The other factors make a difference. If you normally water 1 inch per week and you get 1/2 inch of rain, then adjust and water only 1/2 inch that week.

Mowing
Every week mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. However, bermuda, centipede, and bent grasses will become the most dense when they are mowed at the lowest setting on your mower. In fact there are special mowers that can mow these grasses down to 1/16 inch. Dense grass shades out weeds, keeps the soil cooler, and uses less water than thin grass. Tall grass can feed the deep roots you developed in #1 above. Tall grass does not grow faster than short grass nor does it look shaggy sooner. Once all your grass is at the same height, tall grass just looks plush.

Fertilizing
Fertilize regularly. I fertilize 5 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above. Follow the directions on the bag and do not overdo it. Too much is better than too little*.

At this point you do not have to worry about weed and feed products - remember at this point you are just trying to grow grass, not perfect it. Besides once you are doing these three things correctly, your weed problems should go away without herbicide.

* This used to read, "Too little is better than too much." Recent test results show that you cannot get too much organic fertilizer unless you bury the grass in it.

I believe core aerating to be vastly overrated. You can get much better results by spraying any clear shampoo at a rate of 3 ounces per 1,000 square feet and then irrigating. Do that twice or more separated by a full week or two and your soil will soften up nicely. I have experimented with alternative ways to soften hard soil before and come up with one pretty good one. But this one beats everything I came up with. Here again, using too much is better than not enough. It will just take more apps and longer to get the same softening effect.

Your weeds should go away as your grass gets taller. Many weeds are sensitive to being sprayed with vinegar. You can try spot spraying each weed with full strength vinegar. Unfortunately the grass is definitely affected by that, so try to shield the grass from the spray. It may not kill the weed entirely but it will knock it down and let the grass grow up thus preventing new weeds.

Do you have any shade over the lawn? If not, then if you want to have a great lawn, considering moving some Kentucky bluegrass in. The benefit there is that KBG does not need to be overseeded every fall like fescue does. KBG keeps getting more dense all the time.

If you decide to get your soil tested, Logan Labs is a professional company that does nothing but testing. Their $20 test is 10x better than any university extension service test at any cost...with the one exception of the UMASS test. You would have to pay other labs for tests running up to $100 to get the same test that Logan Labs does routinely for $20. Also know that when you get your test results, if you want to correct the chemistry of your soil, you cannot do that with organic materials. If your soil needs boron, there is no organic replacement for that.