When we moved into this house years ago all we had was errosion like you and high weeds. I bought bags ofSupersoil ammendment which helps the clay and makes the soil more porrous so you can plant and have healthy roots. My favorite tool is a pitch fork which you get deep into the soil and move it back and forth all over the ground but if you have a lot of land rent a bear cat and turn your soil before it gets worse where eventually mud washes into your house. Overwatering doesn't work either. Our neighborsa have tried that and boulders are comming down on the hill. Water well after using the Supersoil

Pure clay is better than mixed.
Try to maintain mulch layer of chips or other slower rotting stuff. Worms and critters will keep the soil diggable.
If you need a hole ASAP, you can dig with pick or mattock (or digbar), but some of the chunks will be very hard.
"dig small holes and fill them with water to soften"
Put out a slow sprinkler set to the diameter you need. Set oven timer (for ?? 30 minutes??) Dig within the next couple days (before soil re-dries)

Others reply...
Spading forks are nice. Avoid the flat-tined, since they bend easily.
"bear cat" [= bobcat (or whatever mfr at your rental), aka narrow suburban tractor, sometimes used indoors :-) ]
Have to tow them from the rental on their trailer. http://www.totalrentalshakopee.com/trucks_trailers_rental.htm http://www.carlsrentals.com/bobct.htm
$overkill for a few holes. :-)

Clay swells when wet and shrinks when dry, explaining the cracks. Your clay is lacking in vegetative matter which would change your soils structure and provide the spaces required for oxygen and water. It will take a year or two but you can make your soil into good garden soil. Don't try and amend the hole for the plant you want to plant at the moment. Bite the bullet and buy truck loads of municipal waste compost. It is the cheapest and you are better off with lots of the cheap stuff than a meager amount of bagged high priced compost. Do your whole yard at once. You should only work your soil when the moisture content is right. This means watering a couple of days in advance of digging. This year you should get enough compost to cover your whole yard to at least 6 inches, and with the soil moisture ready rototill it in. From now on every year you will only need to apply about 3 inches as a mulch to the top of the soil and the soil life will work it into the soil. Soon you will be bragging about how good your soil is and how easy it is to work. Al

I have similiar problems. Also it is important to be careful not to walk on your newly prepped and ammended beds when wet. I had a pretty good bed and got anxious to redesign it after the rain.. before it had dried out. I seem to have compacted the soil.
Basically though (before I compacted that bed) I started with one bed at a time and worked in alot of leaf mold or any other organic stuff I cleaned up around the yard.
For Lavender beds or other things that needed good drainage I worked in some pea Gravel ... before that I killed alot of lavender plants.
The soil does get better over the years. Also I have had good luck with raised beds for veggies. It lets me have better control of the soil.

I, too, have clay in my backyard. Being new to gardening, I started reading and found out about lasanga beds. I built my first one about nine months ago, and what has happened to the soil is amazing. There is very rich soil and a lot of worms, and my plants love it. If you just search lasanga beds on this sight, you will find all the info you need.

Thank you for the suggestions. I was terrified when I saw the crack in my yard, thinking the worst with $$$ to spend. The clay must have been really dried up from the heat. I will try to put new soil in that spot but it is about 6" deep in some spots. Should I wait before planting a tree?