This is a crochet pattern that is very simple, and it is actually for a bookmark. I simply enlarged it. The pattern is found on Crochetroo's blog, and she can also be found on Ravelry. The link is noted in the appropriate place, but I will also type it out (just in case the link doesn't work) as you will need it to make your scarf:
To make this bookmark into a scarf, you are going to use bigger yarn, and a bigger hook, and depending upon the length that you want your scarf to be, you will make more fans than in the pattern. Once you have done a couple of pattern repeats, this pattern- and my alterations- make more sense. You will want to read through these instructions and the bookmark pattern instructions first, just like any pattern. Then all that you'll basically have to decide is what color or color combination & what size of yarn- I recommend going with worsted weight or larger, and the recommended crochet hook for that yarn. For example, use (4) worsted weight yarn, and a 5mm, 'H' hook- I have made this scarf with wool and cotton, so it is your choice.
this photo- photo credit:Getty Images.com
Follow the pattern as written (see the link to Crochetroo's blog above). If you have reached one step away from the end (before adding the picots to the last fan) and want to make the scarf longer, you have a couple of options, depending upon how much longer you want it to be and what size yarn/hook you are using. First, just crochet more fans to lengthen the scarf and once you've gotten to the length you are happy with, finish with the last step. Alternately, if you don't have much more length to go, add fringe...or really long fringe ;) Finally, for a perfectly symmetrical scarf you just make the pattern again (now you have two scarves), and join them in the loops, at the middle. This way you have the fans pointing down at the scarf ends (this is what I did with this scarf, unfortunately I gifted it, so I can't take anymore pic's to show you...) Anyway that you choose to make this scarf, it is an awesome pattern, and very versatile.