I have clay soil, too. You need to add organic material, composted vegetable matter, like grass clippings and kitchen waste, or cow or chicken manure (composted, not raw) or similar material. Do not add sand.
Meanwhile you can grow things like lettuce, greens, herbs, and other things that do not need planted deeply, and which are not root crops. You can also grow wildflowers for your area, which should do well in poor soil.
You can probably grow tomatoes and peppers which have been started at a nursery. It will be tough to start them from seed until you have amended your soil.
Square foot gardens and container gardens are very nice, but will cost you a lot of $$$$ buying the soil for it.