These photos show the technique I used for ending off in this pattern. I like to end off in the back of the work; I think it looks a little neater that way. You don't have to do it this way; you can also end off in the front of the work. I will show you the method I used, but feel free to do it either way.
First, I removed the crochet hook from my work, being careful not to unravel any of my crochet stitches.
Then I turned the work over so I was looking at the back of the work. Then I inserted my crochet hook into the piece and pulled the active loop through to the back.
Then I left a long tail of yarn, about 14 inches long. This length is used for stitching the circles together, and after that it is also used for sewing the covered bottle caps together.
14 inches was enough yarn for these tasks, but barely. In hindsight, I wish I had left a little more -- 16 inches would have been better, and if you want to leave even more than that you can do so. Cut the yarn.