[COLOR="#300090"]There are different ways to count for your increase in the round.
For a round FO that lies flat (like a doily) you increase 7 to 10 times a round depending on the height of the stitches in the round (sc, hdc, dc, tr, etc).
For a hat, you want not a flat circle or disk but more of a dome. Most hats that use a sc or dc stitch will have you increase 6 times per round until the dome is large enough to cover the crown of your head (or of your model's head). Note that if you always increase in the stitch above your last increase the disk will not be perfectly round but more of a hexigon. One easy way to round it out is to place you increases halfway between the increases of the previous round or two.
Here are intructions for making a circle. The same site has a hat pattern using that circle technique.
WoollyWormHead has instructions for making spiral rounds. Which is similar to how you started.
I chained six stitches, crocheted into the first stitch, and then pulled the yarn through that stitch (creating a new stitch; I figured this was how you increase for a new row).
I'm not sure what you meant buy "pulled the yarn through that stitch." To do a sc increase you work two SC in the same stitch of the previous round. That link is to a video on the Coats & Clark website.
Good luck. Crossed Fingers