When working the chart for the first time, start on row 2, and omit the purple stitches (eyes) in the first three rows. When alternating colours to work skulls, bring the opposite colour forward to knit or purl respectively (knit stitches are always knit and purl stitches are always purled). This will create the image on both sides of the scarf, evenly.
At the end of each row, remember to twist the two colours together to create a joined edge – this is what binds together a double knit scarf, with a neat seam up the side.
A note on the chart: The purple stitches are to be ignored in the first and last three rows of knitting. That is the only reason why they are purple; this is still a only a two-color scarf. This is further explained in the instructions.
This is not a good first project to learn double knitting, as it will not be explained in the project instructions. You can learn to double knit here: http://knittinghelp.com/knitting/advanced_techniques/ (scroll down to about the middle of the page). If you: 1) have a handle on the concept, 2) are able to double knit where the purl stitches touch on the inside and the knit stitches lay smooth on the outside, and 3) can read charts easily, then this is a suitable project.