I just did a traditional long tail cast on. 31 stitches. She has a note that when you slip the first stitch of every row, you want to bring your yarn forward as if you are going to purl, slip the stitch, then pull the yarn back to the back as if to knit and knit the next stitch.
Basically you are slipping the first stitch, knitting to the center, slipping another stitch, knitting 2 together, passing the slipped stitch over (this is your decrease) and then knitting to the end of the row, then you knit back to the "beginnig" again and start over. When you get down to having only having 15 needles on your needle, you then cast back on (I just did the simple thumb loop cast on) on each end to bring your count back up to 31. It's all a math game, really.
When you first start knitting, don't think about what's ahead, just think about what you are doing right now. I copy most of my patterns and put them into a word document and use a paperclip to keep up with what row I am on. That way you only worry about what is happening on your current row. This is one of those patterns that you just have to knit and trust that it is going to do what it says it will do.
PM me if you have any questions. I've made a few of these scarves for presents this winter and they do up fairly quickly once you get the hang of the pattern.