well, i don't like to use the word 'correct' because people do things lots of different ways, and they work... but, i've been shown to carry it up the side in a similar way to doing intarsia, you scoop the yarn you are carrying up, so it is 'twisted' round the yarn you are knitting, rather than knitting the 2 yarns are the same time in the first stitch (if you get me)...
Having said that, i NEVER carry yarn up the edge of a scarf, I will only do that on pieces that will be seamed in that area. I would prefer to do hours of finishing than stare at that odd coloured bit of yarn working its way up one side of my scarf, but that's just me
