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You want to leave a nice long tail so you can weave it into your stitches and finish your hat. You should have plenty of yarn left over in your skein, so cut a one-foot tail to be on the safe side. Remove and store your stitch marker at this point. You don't need it anymore for this project. Thread the tail of the yarn through your tapestry needle. Slip the needle into each of the remaining 10 stitches, pulling the free end of the yarn through the stitches. You should slide each stitch off the needle, onto the free tail. When you're finished, all the stitches should be off the needles, and you should have some yarn left over hanging loose. There will be a small hole at the center of the 10 stitches. Pull the free tail to tighten up the end of the hat and draw the stitches close. The hole should be drawn into a pinpoint. Turn the hat inside out, then weave the tapestry needle through your stitches to secure the free end of the yarn. This is called "weaving in the ends" of the yarn. When you're sure that the yarn won't come loose and unravel your hat, cut the rest of the tail off with scissors. Do the same thing to the free yarn at the brim of the hat, where you cast on your original stitches.
Cut the yarn with your scissors. Thread the yarn tail through the remaining stitches. Pull the yarn tight. Weave the free yarn into your stitches.