Before laser levels, and still widely in use, on building sites boning rods were used. These are the T shaped wooden stakes you will have seen on the edges of sites.
So make eight five foot long straight posts with a pointed end and a flat end. Lie them side by side and mark all of them at four feet from the flat end with a line.
Now on a wet autumnal day decide where you want the centre of your circle to be. Scoop out a shallow depression, six feet in diameter but only six inches deep or so and puddle the clay soil by dancing around on it. You may find a greasy auroc skin helps line the pool. If it doesn't rain enough fill the pool with water.
Around the edge of the pool space your eight posts equally and bang them into the ground until the marked line is level with the water. You now have a ring of posts whose tops are level.
Looking across from post to post it is then easy to set up other posts so their tops are also level.
And then you can decide that the top of your sarsen uprights should be so many feet above that level, and you can measure down into the excavations from your level to get the depth of the hole right for the length of the sarsen you have to hand.
As he says, simples. But I hadn't had it explained to me before so it had never occurred to me that that was how it could be done..
More on boning rods at http://www.pavingexpert.com/setout03.html