Your garden space seems to have poor drainage--possibly even visible cracks in the soil--and maybe even an orange tint that swells up and gets boggy when wet. Plants aren't growing well and you're ready to give up on the whole space. You don't have to. Heavy clay soil can be amended easily with a few additives. Doing so will give you a balanced growing medium in no time.
Cut straight down into the garden area with a hand trowel and collect a sample of your soil. Be sure to get your sample away from decaying leaves or old vegetation because these can contaminate the sample and show your soil as being richer than it is. Place your sample in a clean container and take it to your local agricultural extension office or a full-service garden center for a free testing. This test will determine the pH level of your soil and will help determine what needs to be done to your soil to improve it. A heavy clay soil will contain a high pH level.
Consider the area that you wish to amend. The recommendation is to improve the whole garden space or yard at once versus attempting to amend each individual planting site. As the plants' roots grow, they will eventually spread farther than your planting hole. By improving the entire space, you give the right soil for the roots to spread. A heavy clay soil makes it difficult for roots to move through its density.
Collect 6 to 8 inches of organic matter for your intended space. Organic matter includes leaves, peat moss, compost, sand, manure and chemical-free grass clippings. For best results, use a mixture of more than one of these additives. Spread your organic matter through your space.
Mix with a shovel, turning the organic matter down into the clay soil 8 to 12 inches deep. Continue to mix the whole area. Starting with a shovel keeps from pulverizing the soil to too fine of particles right away.
Finish with your tiller or hoe, making sure that the whole area is mixed well. Add more organic matter, if needed.
Plant your plants immediately. Your amended soil will settle as the microorganisms in the soil continue to break down the organic matter you added.