I just posted tis under in a similar topic.
From the sound of it you will want to put in a french drain. A french drain is a pipe burried in the ground with holes in it to let the water in, the pipe should be covered with a special cover to keep the dirt out of it, and then be surrounded by gravel. It should be about 6 inches or so deep. You will need to run it down hill to a spot where the water can drain out, or build a dry well. You can get the pipe and covering at your local hardware store, it is not that expensive, the digging and bringing in gravel is the hardest part.
As the soil is clay you may also amend the soil by adding compost and round sand, if you add sand it must be the round kind as the sharp kind will turn the clay into rock, you need to add lots of it as well.