the shaw you picked is knit in a circle, from the center out. You start out with 9 cast on. On row 2, when you knit 1, YO, knit 1, YO across - the YO means 'yarn over' the needle, making a new stitch - that is why at the end of the row you have 18 stitches. Each row that has YOs is an increase row, that is how the circle gets bigger and bigger.
If you would rather cast on 200 or whatever, maybe you should look at some of the other shaws in the book. Or, here are a bunch to look thru, too: http://lovetobikeandknit.blogspot.com/2006/05/rectangular-shawl-patterns.html