Experts and BHG readers answer.
How to Improve Clay Soil in an existing lawn
The best thing you can do is use a core aerator. This is part of good lawn care anyway, but not everyone does it. Even if you do, it's generally done just once a year, but it can be done twice a year with no problem. Do it when the soil is really moist to make sure you are pulling deep plugs.
I have not tried many of the liquid aerators so i cannot answer for every one on the market. However, my limited experience with products that claim they'll relieve compacted clay has been disappointing. Compaction is a physical problem and requires a physical solution -- tilling, or core aerating.