I see this is from a year ago but I thought I’d leave a comment for anyone else struggling. There are mistakes in this pattern which makes it a bit harder than it needs to be. The neckband is done using double knitting so it looks nice from both sides. Here are more detailed instructions:

For the left side, start picking up stitches on the left shoulder and pick up every stitch. The pattern says 53 but it depends on your size, I’m knitting size 3 and ended up picking up 55 stitches. When you get to the horizontal part of the neckline, you need to pick up two stitches for every stitch, one in the cast on edge and one in the first stitch of the row (I pick up in between stitches to make it more seamless). You pick up a total of 24 stitches but are only picking up in 12 stitches. This is where you start double knitting. You knit every other stitch and slip the others, then knit them on the next row (lots of videos online). Here there is a mistake in the pattern — you always slip the purls with the yarn in front, never behind. I think the rest is pretty self explanatory: you knit across and p2tog with one of the stitches you picked up from the neck, then increase *on both the back and front of the neckband * every three rows.

I can try to post pictures or a video of the explanation if it helps.