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Looks like a nice thick coaster; possibly useful larger as a potholder.

The coasters and the basket with lid are done in rope-crochet = crochet stitches made round rope. Yarns used: any yarn will do: from lace weight taken double or triple, to bulky. The definite size depends on the rope you'll use inside of your stitches and on the yarn used. You can make something fine and delicate as well as something sturdy. I worked with two strands of lace weight leftovers from shawls - I changed often one strand in color, so that I obtain that 'tweedy' effect. The final size is as you decide it's got to be -- no gauge needed but you'll need to crochet with a smaller hook than normally done with that yarn, because the stitches need to be tight to add some solidity.

While this is a pattern for a coaster, the spiral design could be used as a motif for something else also

This tutorial just uses stones and felt.

I've also seen a suggestion that one could stiffen up the trivet by sandwiching a CD in between the two pieces of felt. Though that would make something closer to the size of a coaster than a trivet.

One could also use those flat glass pebbles instead of stones.