A couple of pointers (so you don't make the same mistakes I did).
To begin with I found circular weaving a bit tricky. As you can see from my first attempt above I struggled to find the correct tension as I tightened my yarn. I didn't realise anything had even gone wrong until I started cutting and tying the warp threads together and my weaving began to curl. The best way I've seen it described is to pull your yarn until it fits snugly rather than tight, try to resist pulling it as hard as you can.
If you find you've made a mistake it's really easy, although a bit frustrating to fix. I kept forgetting to go over or under an extra warp thread ever time I reached the starting point. If you do this all you need to do go back and reverse your steps. I think the thing I love most about weaving is how easy it is to go back and fix any mistakes or problems.
The first coaster and the mistake above each took a couple hours to finish. Once I'd had a little practice I was able to complete a coaster in under an hour.
As you get to the end of your cardboard circle it can get harder and harder to weave. I found it was easier to make sure I had plenty of room left between the edge of my weaving and the cardboard rather than weave close to the edge. I used a dinner plate to make my template as this seemed to leave a good amount of space at the edges. This is something to bear in mind depending on the size of weaving you want to make. If you wanted to make a circular weaving as a placemat or rug you would need a much larger size template.