I'm a fairly new knitter, and haven't tackled knitting in the round yet. So when I'm doing the seam on a hat, is it possible to finish it in a way that the seam doesn't show when the cuff of the hat is turned up?
Yes, seam from the top down, using mattress stitch (about 2/3 way down the page) until you get to however many inches left - the amount of 'turn up' your cuff is going to be. Then switch to seaming on the inside with the wrong side showing and you should have pretty much an invisible seam.
P.S. Don't be afraid of knitting a hat in the round - once you get the hang of it you'll never go back to knitting hats flat.