sorry if a little obvious, but how about inserting it into the ground with a shovel or spade ?
Ive done this very sucessfully and planted courgettes etc through it.
I first selected a piece of plastic that was much larger than the area to be covered, laid it out with equal overlap, then work your way round with a shovel, push down until the plastic is well buried and taut. Keep going round and round until the plastic is as taut as you want it. This method does use much more plastic than the area covered, but a small price to pay i think. its very quick, and if it comes loose (which it shouldnt) just push it back in again. The only thing i did do was stand a rhubarb forcer on each corner for good measure (but i dont think it would move anyway !