First you should probably recontour the ground to make the water run away from that area. Not too many things like to have wet feet and stand in water. If you are getting water under the house you may want to install a french drain.
Changing clay to soil is a long term project but can be done. if you contour your ground correctly you may just want to put a layer of top soil on place of some of that clay. But , again you will have to change the contour so that there is not a pool under the top soil and the top soil does not wash away. All that being said, if you want to create good soil from the clay you will need to be patient and be ready to do some work.
You will need to amend your soil with lots of organic matter, Peat moss, leaves. compost of all kinds, manure. When we decided to plant a garden in a patch of clay we literally added tons of material over a few years. We collected other peoples leaves from their curbs in addition to lots of our own. we brought in truck loads of composted manure. (My kids played king of the compost pile). You will also need to add lime every season to adjust the PH. After a while you will have nice dark rich soil.
You could also try growing something that likes poor soil the first couple of years. Maybe Thyme. So it's thyme or time :)