Quick question on a pattern

I am making fingerless gloves from a pattern found in the book "Vogue Knitting, Teen Knits. On the go"
The part I am stuck on says “Work 4 rows in St st and stripe apt. Inc 1 st each side on next row, then every other row 4 times more”

What I want to know is am I supposed to knit/purl one stitch and then cast on or cast on first and then finish the row?

You’re not actually casting on, you’re increasing. Any of the increases found under the 'Free Video’s Tab at the top of the page will work. But yes, you do get a better finish if you do your decrease one stitch in from the edge.