For the first one I hemmed the raw edge under and then turned it under again and sewed that down. Very secure!
But for the others I decided that wasn't necessary. I trimmed 1/2" off each corner, turned the edge over once and pressed. Then I turned the edge over once more, mitring the corners as I went, pressing that down firmly. Then I was able to just sew the hem in place. I happened to have the exactly right blue thread in my box.
They turned out very well, and are a lovely soft cotton, woven with dyed threads so both sides are the same (except for the hems turned under).
There is a Sunbeam iron here that steams very nicely, and turns itself off if not used for a while.
All in all (though it took longer than I expected) a happy result for the first sewing project in Arizona.