I suggested trying the tyvek tape but haven't tried it myself.
I've had good luck with tape in general, however, when there isn't much tension on the pull outs. I assume that use as a ground cloth would require very little tension on the pullouts.
In recommending tape I was focusing on the key word "easiest" in your original post. I would experiment with, say, an 8" long piece of 1" wide tape. Putting a 2" long piece of tape at the midpoint of the 8" piece (sticky side to sticky side) will give a non-sticky loop for the stake. The remaining two 3" tails can then be sandwiched over the tyvek corners.
I've had very good luck with strapping tape also. It'll stick to most things.