Dig into the soil when the moisture content is just right. Too little moisture and the clay will break into fine particles, too much and the clay will clump together in large, hard particles. Both are bad for soil tilth, or the ability to maintain plant growth around the roots. Squeeze a handful of soil from just below the surface. If it forms a solid mass that is not willing to easily break apart, the ground is too wet to work. If it has no moisture at all, it is too dry. If the soil forms a ball that is solid but easily falls apart when poked, it has the right amount of moisture.
Place the top 6 inches of the soil from the garden on a tarp. This may be easier if done in small sections if the garden is large.
Rake through the soil, removing all the large rocks. If necessary, use your gloved hand to pass through the soil to remove smaller rocks. It is not necessary to remove every small rock from the soil, as new rocks will constantly work their way up from below.
Divide the soil on the tarp into 3 equal areas. Add compost to the tarp that is equal to one of the areas and then mix the 4 piles together. That adds about 25 percent organic material to the soil, which allows the clay to release its nutrients much more easily and causes better water management.
Shovel the soil and compost mixture back into the garden and, if necessary, dig the soil out from another area and repeat the process.