Thanks for writing! The very best thing you can do for clay soil is add lots of organic matter to it. Compost, peat moss, shredded leaves, etc. are all great sources of organic matter. Compost is free if you make your own, and you should be able to find other sources of organic matter at low or no cost in your community. For example, check to see if your town has a free compost facility. Also: A lot of woodworkers have tons of sawdust they're often willing to let you haul away for free. Just add the sawdust to your compost pile and you're set. Alternatively, the Starbucks chain of coffehouses gives away their old coffee grounds. Just add those to your compost pile. You can often make a deal with friends/neighbors/etc. to haul away the leaves they rake up.
I hope this helps. Good luck!
---Justin, Senior Garden Editor, BHG.com