I agree with the earlier posters, do not work the ground if it is really wet. I learned that lesson last year i tilled with a tiller and the clay just balled up and turned to iron when it dried. We also invested in both of the tools posted earlier, I am not sure gardening is posibble without a spading fork. I purchased a 4 prong cultivator for DW to use and she loves the thing, barely will let me touch it, She says I will lose it or break it LOL. It sure does work well for keeping the soil around the plants loose and workable. I agree cover it and let it dry a little if you can.
It may have a little clay in it, but not much...the clods are really just dried organic matter feels almost like a dried up clod of peat...very light and almost paper mache tough
Without a tiller you're gonna wear your arms out. If you have a stable nearby give 'em a call and see if you can dig from their manure piles. It only takes horse manure 4 months to decompose enough so it won't burn out your crops, and you can use it sooner if you mix it. We horse owners buy our grain in plastic bags now--it's industry-wide. Barns have to get rid of both manure and grain bags, so they'd probably give both to you if you do the labor. You can fill bags, roll the top down and duck-tape them shut and even transport in the trunk of your car without worry that they'd split.
I'd love to use a spading fork. it doesn't compact the soil at the bottom like a spade does but unfortunately my ground is full of rocks that are just the right size to jam between the tines. Last time I used one I had to get a hammer to get one unjammed.