To create a border on an Amigurumi you use a technique that is called Surface Crochet.
This technique is used on many of by Amigurumi crochet patterns. I have created a tutorial and a video on how to surface crochet. You can find the video below the written tutorial.
This is how you surface crochet:
Photo 1 & 2: Insert the hook under the first stitch, grab the yarn and draw up a loop.
Photo 3: Yarn over and draw through the loop on the hook attaching the yarn to the body.
Photo 4 & 5: Insert the hook under the next stitch.Yarn over and draw the yarn under the stitch and through the loop on the hook (like a slip stitch). Do this in all the stitches.
Photo 6, 7 & 8: Sew in the last piece of yarn like on the photo to finish the border.
For more help, watch my video on how to surface crochet on an Amigurumi.
Which is a very detailed step by step video tutorial.