The scarf you are wanting to make uses a technique called 'Illusion Knitting'. The chart for it is a bit different than your average knitting chart. Generally speaking, you will read charts starting from the lower right corner (row 1) and work right to left for right side rows, and then left to right for all wrong side rows.
In illusion knitting, you will also be using 2 colours which will be worked 2 rows at a time. According to the chart for this pattern, all RS rows will be all knit stitches, so that's easy. It's the WS rows that you'll have to concentrate on a bit more. If you have the 'chart 1' open, take a look at row 2 of the chart, which will be read left to right. It has 14 plain green blocks, then 2 green block with a dot, then 15 plain green blocks. If you look at the key for the chart, this would be translated into: Purl 14, Knit 2, Purl 15
Also, maybe take a look at this link which goes into more detail on illusion knitting.
Hope this helps.