It's a little difficult to say without seeing the scarf laid out but it looks like the body is a garter stitch triangle knit on the bias, starting at one corner. The edging may be added on at the end by knitting a strip for a number of rows, again in garter stitch, and every so many rows extending the row to the body and knitting the last stitch together with a stitch picked up from the body of the scarf. ir is a pretty look.
There's a way to do it that lays in those eyelets for the ribbon, but I warn you, you're going to have to think a little. It's not hard, just something I've seen people trip over. If you have any doubts, try it with a small ball of scrap yarn first and make a doll-sized shawl. The directions will work out the same whether it's six inches long or big enough to wrap up in.
You'd need whatever yarn you want and needles to fit it, and you need a stitch marker and a safety pin or a scrap of other-colored yarn to mark the right side of your work.
Cast on eleven stitches. Knit ten of them and slide your stitch marker onto the needle. Yarn over and knit the last stitch. Turn and knit all the way back. Turn and mark what you're looking at as the right side of your work.
Now this is where people can get mixed up:
1. knit just the first ten stitches, right up to the stitch marker, then
2. turn the work and knit back. Don't wrap and turn or anything--you want the hole at the edge of the ruffle.
3. On the next row, knit the first ten, slip the marker, yarn over and knit the last stitches.
4. On the next row, knit across.
If you repeat those four rows, you'll end up with a triangle with one ruffled edge. When it's as long as you want it, instead of Row 3, use these instructions:
Knit the first ten stitches, slip the marker, yarn over and knit three stitches together.
That will remove one stitch per row (the yarn over and one decrease cancel each other out) and bring the triangle up to a point. You should see a line of eyelets along the edge of the ruffle. That's where you weave the ribbon or other color of yarn through.
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