Whenever this question comes up on the Vegetable Gardening forum here the common recommendation is to put something under them - cardboard, layers of newspaper, a board, or best, a thick layer of straw mulch. Of course if your plants are already well mulched as they should be then it is just a matter of laying down more mulch under the fruit. The point is to get them off the ground.

Check out the Vegetable Gardening forum for more details, ok?. The focus of this forum is canning and preserving.

Dave

I've found that the green plastic 'mesh' baskets that fruit frequently comes in work really well if turned upside-down and placed under a squash. They hold the fruit up off the ground so they stay dry; also seems to deter vermin.

A clay pot upside-down works too.