Answer: You didn't specify whether you are growing a vegetable garden or a flower garden. The answer to your question would be different for each. Since you know that the site was at one time a landfill, it might be prudent to build raised beds in which to grow your veggies. Raised beds can be filled with uncontaminated top soil and organic matter (aged manure, compost, etc.), and you can plant veggies to your heart's content without worrying about what might be in the soil. Raised beds will drain well (and warm up earlier in the season so you can plant sooner), which will solve the drainage problems. The organic matter you mix into the top soil will hold some moisture and provide some nutrients to your plant's roots as it breaks down. Raised beds do not have to be fancy - simply mound up the earth and slope the sides to prevent erosion, or use planks around the sides, or concrete bricks to keep the beds intact.
If you're growing flowers rather than vegetables, you can improve the clay soil by incorporating lots of organic matter. I'd rototil the planting site up, spread a 4-5 inch layer of organic matter over the top, and rototil it in. Then level the site and plant. After your plants are in, cover the exposed soil with a 2-3 inch of organic matter to help suppress weeds and moderate soil temperatures. At the end of the season, dig the mulch material into the soil and add a few inches of fresh mulch over the top. In the spring, before you plant, rototil the old mulch material into the soil, plant, and add a new layer of mulch. After a few years of incorporating organic mulch, your clay soil will turn into wonderfully rich and loamy soil.
Best wishes with your garden!
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