I have made a lot of these in various shapes and sizes, including variations for small, handle-less teacups. Those do double duty - they insulate the cup, keeping the tea hot longer, and prevent burning your fingers when handling it.
I made these three in one evening.
As you can see, they're not just for pop cans, even though they're all the same size. :-D
These can be made in any material you'd like, but my preferance is for Bernat Handicrafter Cotton Ultrasoft, which is often marketed as dishcloth yarn. It's 100% cotton and machine washable and dryable. Though the label recommends a 4.5mm hook, for these I use a 3.5mm hook. This makes them better able to hold their shape when they're empty.
For a cooler that fits an ordinary pop can, using the yarn and hook size I did, this is how.
Start with 8sc into a magic ring. DO NOT JOIN. The rounds are worked in a spiral.
Increase each consecutive round to make a flat disc as big as the bottom of a pop can. For these, that worked out to 16sc, 24sc , 32sc, 40sc in each consecutive round.
After this, you can just keep working 40sc rounds, but I like to do the first side round in the back loop of the last disc round. You can see that round in the second photo. I find this gives a more defined crease between the base and side rounds. Either way, just keep going until the cozie is the height you want it to be. Feel free to change colours and add texture stitches as desired. As you work up the height, put a can (or whatever you're making the cozie for) into it every now and then to check height and fit.
If you find that the fit is a bit snug, making it hard to put the can into the cozie, try doing 1sc, 3ch, 1sc in one stitch, evenly spaced around the top of the cozie. It gives a slightly fancier looking cozie, but it also flares out the top row enough to make it easier to put a can in, while still keeping the rest of the cozie snug enough not to fall off too easily when the can it picked up.
The first one of these I did was the dark blue with light blue stripes and textured stitches. I was just playing around as I worked. I got positive responses from the family over it, but my personal preference is for simpler designs, so for the others, I stuck to the basics.