I'm not 100% clear on what your pattern looks like. Is the front of the neck edge just a long flat span, like from shoulder to shoulder, and then the sleeves continue up over the shoulders? This is what I'm picturing, if I'm not right, let me know, because I may not be advising you correctly. Here's what I think you're supposed to do....
You're supposed to work until you reach the bottom side edge of the neck. You abandon the yarn you've been using, and, working with a new ball of yarn, you bind-off the stitches they tell you (regular knit bind-off will be fine, unless the edge needs to be stretchy. Since binding off can be quite tight and inflexible, use a larger needle to do the bind-off. You can go up three needle sizes or more! Just try it: do a few stitches, and see how the bind-off looks.) Anyway, when you're done with your bind-offs, you are now on the other side, where the other sleeve continues. Using your normal needles again (!), follow the directions for knitting that row to the end. I assume the back is a separate piece? So, at this point, you'll turn the work, and knit with that same yarn, back towards the neck edge. When you get to the end of this row (you've reached the neck edge), just drop this yarn. There are the stitches from the other side of the neck, waiting for you, with that other yarn. Work with that yarn to the end of the row and back. Then use the other yarn.
So you do two rows in a yarn, and then switch to the other yarn. This isn't necessary; you could work one half at a time. But some prefer it, because it requires less thinking: you follow the same directions for both halves at the same time (mirror image directions), so you can knit longer before looking at your pattern again, and it can be faster because of that.
Hope that answers your questions!