The yarn you use and needle size probably doesn't make a lick of a difference. I used Vanna White's line of yarn because I loved the color, it was super soft, and cheap. It took 1 1/2 balls of yarn. I used size 10 1/2 needles (6.5 mm).
sl1kw: slip 1st stitch knit-wise
sl1pw: slip 1st stitch purl-wise
BC: place 2sts on a cable needle in the back, k2, k2 from cable needle
FC: place 2sts on a cable needle in the front, k2, k2 from cable needle
Cast on 30 stitches.
Row 1 (WS and all other wrong side rows): sl1pw, k2, p2, k2, p16, k2, p2, k2, p1.
Row 2: sl1kw, p2, k2, p2, k4, BC, FC, k4, p2, k2, p2, k1.
Row 4: sl1kw, p2, k2, p2, k2, BC, k4, FC, k2, p2, k2, p2, k1.
Row 6: sl1kw, p2, k2, p2, BC, k8, FC, p2, k2, p2, k1.
Repeat rows 1-6 until desired length.* Cast off while following the WS of the pattern, it looked most natural casting off after Row 2.
*My favorite rule of thumb for knitting scarves is to knit the scarf as tall as you are (or whoever will receive the scarf). That made mine about 65 inches long, but knit it as long as you feel like. It's such a fast knit and makes a very cute slinky skinny scarf so if you have the yarn just keep on going! ^_^
Fringe: I cut 12" lengths of yarn, 6 per fringe section, and 5 on each edge. That's 60 in total. I folded the yarn length sections in half (6 pieces), stuck them through the scarf at the cast on and cast off edges (just make a hole and squeeze it through or use a crochet hook), pulling half way through, making a loop then pulled the loose ends (that are hanging out the other side) through the loop and pulled tight. I hope that makes sense, but it's essentially just knotting the fringe onto the bottom. It's the easiest way to attach fringe, one can even call it the cheater's method it's so simple :-P
Hope you have fun with it! I'm putting the pattern up on Ravelry, and if you knit one up I'd love to see your pictures!