Confusion over confusion.
double knitting is a hole nother bag of beans
you cast on the stitches as said. you work the chart. At the end of the row, you turn your work around and work back. At the end of that: again. and so on.
RS is right side, that refers to the side that is the "good" side of the scarf, mostly with pieces it is the knit rows (but does not need to be)
WS is the wrong side, that is the backside of the garment, often the inside of a sweater and so on. Often that is the purl row.
Some garments look the same from both sides (like in garter stitch) but they still call it RS and WS, since you have to name the sides somehow.
double knitting produces 2 RS sides, by looks. And double knitting with just one ball of yarn and one color seems rather like a lot of work than like a stunning project. But this here is not for double knitting, so forget about that piece of magic for a while.