Well, I looked at your picture and I'm not sure what the part about the "snap" is, because I don't see any snap anywhere.
Cut yarn, thread yarn needle with yarn end and slip the 3 stitches onto yarn needle. Draw up tightly and secure.
This just tells you how to finish off the i-cord. But I'll try to explain a little more (in a second).
Here is what I would do based more on the picture than the directions, although it may be what they mean as well. First I'd finish the i-cord. Cut the yarn, leaving a good tail so you can use it to sew as well, let's say 9" long at least (longer if your yarn is real thick). Thread that tail onto a blunt, big eyed sewing needle. Hold your knitting needle with the i-cord stitches on it like you would to begin another row of i-cord, but instead of knitting this time run the threaded needle into the first stitch you would knit into in the direction you would to purl, and on through the other 2 stitches. Take out the knitting needle and pull your sewing needle so that the stitches are on just the yarn. Pull on the tail tightly to close the i-cord.
Now to attach the fastener. Lay the bar of loop at the end of the fastener across the i-cord about 1/2"-3/4" from the end of the cord, positioned the way you want it to end up. 1.Thread the sewing needle with another length of yarn, and sew over the bar of the ring 3 or 4 times sewing all the way through the i-cord (for strength). 2. Now fold the i-cord down over the bar and using the tail from making the cord, sew the folded down part to the body of the i-cord. Again I would sew all the way through the cord and I'd sew it all over, up to the bar, turn and in a slanting line to the left edge of the cord then across the edge, then in a slanting line across to the bar at the left and then down that side so it made a square of stitches with an X in the inside. Dogs are strong and I'd want it attached as well as I could. Cut your yarn and work in all tails into the inside of the i-cord. If your dog is well trained and doesn't pull a lot or is very weak
you could probably skip part 1.