Where do you live? (if you put that info in your GW profile then we can stop asking that question. It is almost always necessary to understand your issues and not pass out Florida solutions for Wisconsin problems)
What kind of grass do you have? and want?

Growing grass with an active dog in the shade is a losing battle. When the dog settles down, then you can grow grass there. One good thing is that weeds won't grow there either.

As for the organic program, go to the GW Organic Gardening forum, find the FAQs, and at the bottom of the list is the Organic Lawn Care FAQ. That will answer some of your questions and a lot more you have not asked.

Best thing to get from a feed store is the cheapest ground up grain, nut, bean, or seed that you can find. When I wrote the FAQ, corn meal was the cheapest. Nowadays it is the most expensive. And that varies depending on where you live, because shipping costs are a large fraction of the price. Currently for my area, alfalfa pellets (Purina Rabbit Chow) is the least expensive.

Another tool I use and would not be without is an Ortho Dial Sprayer. I use it to spray soap and molasses to soften the soil. I don't use it much but there is nothing else as easy or reliable as far as I'm concerned.

Okay I just found you on another thread - East Kansas. You are probably growing fescue in that location. That is the only shade grass that will work. If you want a dense lawn, fescue must be reseeded every fall until you get it as dense as you want. Watch it at the beginning of every August to see if it has thinned out any and whether you need to add seed.

For best results, find out what variety of grass you have and use that seed. If your lawn was recently seeded or sodded, keep the seed or ask the sod guy what seed he uses. You need the specific variety as close as possible.

I fixed my profile now that you mention it. I like the idea of the soap and molasses to soften the soil. They have mostly bluegrass in their back yard (sorry, I forgot to mention that) right now.

I wonder if I should try overseeding each year with fescue instead of bluegrass? I would probably prefer fescue but haven't had as much trouble with brown patch on bluegrass, so that becomes a tempting solution as well.

Part of the back yard was sodded last year and part of it is established. The front yard looks like a mix of K-31 type fescue and bluegrass. Unfortunately, I'm not sure the dog will ever slow down - at least not any time soon. *sigh* I thought it was kind of a losing battle.

Thanks a lot for the tips on the organic fertilzer. I really like the idea of doing that.

thanks!

I suppose its up to the owner to say what kind of grass he/she would like to see on his/her lawn but I find that, where possible to grow, a combo of grass types is the best way to go.
A 40% Kentucky Bluegrass, 40% perennial ryegrass and 20% fescue, can make for a tough lawn that can best stand up to whatever nature throws at it. When using one type, if the circumstances arise that doesn't suit the type, then you are left with a lawn that is brown, or very thin, or not growing, or.....usually what ails the type.

With proper growing medium, the combo will give good results.
But....there's the rub. No grass, not even the ones suggested to grow best in shade, can grow where the conditions exist how you describe....100% shade.
Grass is a sun-lover....the more the better and planting seed designed for shade, and no sun, is just wasting your efforts and money.
Improve the sun coming into the yard. That may be as easy as cutting the lower branches of any trees that bar the sun rays. Opening up the canopy of higher branches will also help.....but don't climb a tree in an attempt to do this if you are not experienced in cutting upper branches. A broken leg....or worse, is far more expensive than hiring a person to do it.

As far as obtaining the soil that encourages growth....can be as easy as injecting organic material into the ground.
A rototiller might be employed...dig down 6", add the organic material and look to drainage when levelling.
Organic material can come from any circles...usually a hefty portion of compost mixed with other material.....peat moss, coarse sand (not play sand or beach sand), topsoil (not clay)newspaper strips, cobs of corn etc etc, can help the ground retain moisture.

In your area, being in the middle part of America, you can look to use cool season type grass seed or warm season type...or a combo of the two.
But....improve the sun conditions first.

Clover can indeed be used in place where grass just refuses to grow....but clover cannot grow in shade.
While clover has many benefits...it stands up to dog urine, doesn't need fertilizing, (actually can feed nearby plants) by fixing nitrogen right out of the air.
Doesn't need mowing half the time, uses less water...and does bring about more laundry use because it stains more.
But give it time and it will take over a lawn...yours and your neighbors.