A partial solution is to aerate your lawn. This provides an opportunity for water to soak into the ground instead of just running off and down the street. It also allows nutrients, and roots, to penetrate. If you do nothing else, at least have your lawn aerated once a year. It does help.
Early spring is the best time.
Beyond aeration, soil amendment is the most viable solution. For most of us, it is simply too expensive to have the old dirt excavated, hauled off and new topsoil hauled in. My first attempt at soil amendment was something less than successful, but it taught me a lesson. I will pass it along so you can save yourself some trouble. It was my observation that sand was the most porous medium to plant in.