Okay, realizing that my response wasn't that helpful, I thought I'd better come back and say something more useful. So I've looked at the pattern. There are two things you can make in this pattern, a "cuff" to go around a cup like that for hot coffee or you can make coasters. Both of these things are made with a snowflake motif.
For the cuff, they tell you to cast on 60 stitches over dpns OR over 2 24" circular needles. If you knit in the round with two circs, there's no real reason they need to be 24", I don't think.
For the coasters, the writer of the pattern is saying that if you make four coasters, this number will fit nicely around a 24" circular. You can make fewer coasters using a smaller circular or more using a larger circular or you can make these with double pointed needles or two circs as well. But these are also knit in the round. They are done by casting on a multiple of 28 stitches and knitting the snowflake motif in that multiple. Then after felting, you can just cut the circular piece you knit into the 28 stitch pieces, and each of these can be used as a coaster.
For the coasters, there is no need to do any increases because they are just rectangles. If you are doing the cuff for a cup holder, then you do the increases as shown in the chart. You will increase at the beginning and ends of the motif. You will do this by casting on another stitch at the beginning or end of the motif, and your method of cast on will be the backwards loop method. There is a video on how to that here:
The color you will use when you are casting on this extra stitch will be determined by the chart. So for example, you work from the bottom to the top, right to left on all rows of a circular chart. You will notice that row 11 is the first row that there is an increase on. The increase at the beginning of the motif is done in blue, so you will do a backwards loop cast on in blue. At the end of the motif, you will do this in white.
Sorry if I sounded a little snappy in an earlier post. Truly, though, this pattern is written fine as far as I can see.