How do I make an item larger than the pattern indicates?

My next project will be the Infinite Beauty Cowl at I will be using the yarn called for in the pattern, but need to make the cowl a bit larger, as I am bigger than the pretty little model! How do I increase the size? Bigger needles or do I figure out the pattern repeat and increase that way? As you can tell, I am new to knitting.

Those are two good options for increasing the size. The pattern just requires an even number of stitches (pattern repeat is 2) so that may be the easiest way to control the size that you make. See what gauge you get with your needles and yarn and adjust if necessary by changing the needle size. Then you can figure out how many more sts to add for whatever diameter you’d like.
I don’t understand why, under Finishing, the instructions tell you to slip stitch the first row to the last row, doubling the thickness of the cowl. It doesn’t appear doubled in the photo. You can decide whether you’d like to do this or not however. It will look beautiful and be fun to knit, just keep track of stitch number with some markers so you don’t miss a yarn over!