Plan to add compost, and lots of it. The organic matter will lighten up the clay, probably improve drainage and fertilze. Just make sure you know where it came from (a lot of gardeners around here poisoned their gardens with compost that had residual herbicide that had been spread/sprayed on hayfields, hay fed to cows, cow manure sold or given to the composing place, then sold all over the county through various garden stores. The herbicide apparently has a half-life of something like 6 years.).
Before you add anything other than compost (like lime, fertilizer, etc.) get a soil test. Should cost $30 or so for the test, then you can either research the results vs ideal levels yourself for what you plan to grow, or check with you local county ag. extenision office or a fertilizer supplier for interpretation and recommendations. If lime is needed, it's best to apply before tilling, else it takes a few years to affect the soil a few inches below the surface.
As for tillage, recommendations given here are usually disc plow or bottom plow to break up the sod, then disc, harrow, or rototill to break up the clumps. It depends what's currently growing there, and if it's rocky. You mentioned clay... timing can be important so you don't get stuck in the mire you'll make if it's wet, or think you're trying to plow concrete if it's too dry.