(Hey guys - special shout out to those visiting from crochet concupiscence!)
This method uses the double crochet foundation row method with a slight variation. For the standard DCFR (double crochet foundation row), you pull up an extra loop (or chain 1) before completing each double crochet so you can avoid chaining at the beginning of a project. (You can also use SC or HDC for this!)
In order to make a ring with a hole in the middle, you alternate chaining one before the double crochet and omitting the chain to create a DC2tog stitch. This is for the smallest size you can make (24 stitches). This is replicating row 2 of a typical circular crochet pattern (DC 12 in a ring, DC 2 in each DC from round 1).
You can use this method to make any size ring. Figure out which row you would be on and what the total stitches would be, as well as what the pattern would be, and work that as a foundation row rather than into a row below.
So for example, to make a ring with 120 stitches (row 10 of a typical flat, circular crochet project), you would make a DCFR with the following pattern: Chain 3, DC in the first chain (your first inc is complete), DC 8, (inc, DC 8) x5.
This leaves you with a nice finished edge on the outside and inside, and you don't have to chain to start. Variations on this pattern are endless.