That is a cool pattern! Welcome to KH.
Here is a video of how to do short rows w/ wrap.
When you knit in garter stitch, you don't have to 'pick up' the wraps since they won't show.
When you work this pattern, knit the required number of stitches; bring the yarn to the front between the needles. Slip the next stitch. Bring the yarn to the back between the needles; slip the stitch back to the left tip.
Then turn your work and knit back and work the next row.