What can I do to a clay soil to make it ready for a watermelon plant?

Mix sand in with equal amounts of clay.

conpost I think. I think they like acidic soil

I am not an expert, but my childhood home had a heavy clay content, and we used to spit watermelon seeds off our front porch. We had a few volunteers (33 lb and 20 lb) grow from that.

Now, in that same spot, Dad grew cherry tomatoes,and we couldn't get to the fast enough before they fell over and rotted and grew a new generation of cherry tomatoes.

My guess is that maybe a mulch of compost would be enough. The vines did grow toward the compost pile.

Nothing! How deep do you plan to amend the soil? The roots are going to go down several feet. Unless you're going to amend down that far I wouldn't do anything. I would use newspapers/mulch/ground cloth to keep the Mellon from laying on the soil. use 10/10/10 lightly to fertilize through the growing season. And water deeply. If you're growing on a commercial scale have a soil test done. they will give you advice based on what you're growing. But as a homeowner, if you don't amend down far enough/plow/till which isn't as practical... those roots will only stay in the amended area And as soon as you go away on vacation. It'll die. I say tough it out in the beginning when you're watching, watering and caring for it. As soon as it catches on you can let it go and rest easy knowing it's growing in your native soil. No surprises!

If you are growing from seed, at least amend enough area so that it has a good start for its roots as it germinates. If planting just a couple of plants, amend at least one foot below and around sides to give roots a good start. Once the plants have a good hold and grow stronger roots they many be able to penetrate the clay. All you can do is experiment and go from there for next year.

Keep hay on hand to out under the melon once it starts so melon isn't on the ground. You might also want to 'carefully' turn melons after they get a certain size