Soil compaction can happen for many reasons. The first step is to know your soil, and not jump right into solutions for a problem we don't fully understand.

As a farmer, my advice would be:

#1 Analyze you soil for profile, pH, organic matter and macronutrients. Show the results to a professional and ask for advice. Most lab analyses parameters will stand for a couple of years, so it pays off. Besides, doing the wrong thing once can ruin you soil for decades.

#2 Look around. Is the problem uniform for a wide area or is it just you? Are there any water sources or creeks nearby? Cattle grazing? Is there a history you can check?

#3 Choose your crops having in mind the resources you have. Maybe you soil is terrible for a given crop and quite good for another. Maybe you should just let it be, or maybe not.

#4 Don't go online before speaking to a professional. Avoid guru-based farming/gardening, and be skeptical as a rule of thumb. This applies to my own advice as well.

I know a garden isn't a farm. But still, it's about doing things right and achieving results rationally, isn't it?