I don't have Cathy's experience as a MG, so take this simply as my recollection of what I did.
I certainly had very heavy soil when starting out. I had a horse, so was lucky in the sense that I could let the manure mature each year and add it. I also had my own compost bin. Then I'd buy other amendments, such as peat. I always waited until it was relatively dry - the window in the spring is short in my past experience. Either you get to it before the rains start (which I rarely did) or after they stop, which I almost always had to do. I'd take a quick pass with the rototiller, then add amendments, then till thoroughly. Each year I did the same thing until I had lovely soil. It took a couple years to get good soil and several to get great soil.
Lastly, in the fall, if I would remember and had time, I'd occasionally clean the bed and then plant a nitrogen fixing plant like vetch. In the spring, I'd till it under. Another source of organic matter that both added nitrogen and lightened the soil.
I just did a search to see if what I did was in line with current methods. There are some great discussions on the
garden web forum such as the one I just linked to (there are many others there, too). While looking, I also found this
pagewith an interesting way to test your soil for composition - a glass jar and water, with a bit of Calgon!
Just my experience, but found that most inexpensive soil pH tests were wildly inaccurate and had to buy a decent meter. Also seem to remember that you need to test in multiple places as it can vary.