I tried to knit a hat on straight needles (the pattern calls for straight needles). However, the stitches kept slipping off the steel needles and I had to unravel it. A friend suggested I knit it in the round to prevent this from happening and to avoid sewing a side seam. The brim of the hat is done in a mock cable pattern on the wrong side so the pattern shows when you turn up the brim. It is my understanding there is no “wrong side” when you knit in the round. Would I have to knit the brim on the straight needles, then transfer it to the circular needles to ensure that the pattern on the brim appears on the right side? Are there any other pattern adjustments I would have to make? I have only been knitting since April, so I don’t have alot of experience with these things.
Knitting In The Round
To knit a hat in the round you need a 16in circular needle and some corresponding size double pointed needles (DPNs). You need the DPNs when you get into the decreases because the knitting will no longer fit on the circular. It’s very easy to use them on work that is already started like a hat and a great way to learn to use them.
You can do ribbing, rolled brims, cable or whatever right on the circs. No straights needed at all. When you work in the round you do have a right and wrong side technically, but either side can be used. One side looks like stockinette and the other like purl. All you have to do is knit though, no purling except on the ribbing!
If you use a pattern that is meant to be knit flat you may need to make adjustments, but there are plenty of patterns for hats in the round so no adjustments needed for those.
OK let me see if I can explain this… when you knit in the round, you do actually get a right side and a wrong side. You just never switch between knit stitches and purl stitches to get stockinette stitch. So to change a pattern knit on straight needles to one knit on round needles, you have to reverse the stitches in every other row. You do them backwards and switch anything listed as knit to being purl, or vise versa. For example, if you had a straight pattern that said “Row 1: k2 p2 k3 p7 k2” and “Row 2: p2 k6 p3 k2 p2” you would do “Round 1: k2p2k3p7k2” and “Round k2 p2 k3 p6 k2”. I hope that made some sort of sense… I just switch patterns back and forth between straight and round in my head so its hard to explain the process.
You do NOT need to purl to get stockinette when knitting in the round. Since you are only knitting on one side of the fabric all you do is knit. 
That being said, there will be some patterns like cables that you will need to do some purling, but for a basic hat all you do is knit.