The first shirt I on which I extended the side vents, I tried on, then put a pin at the top of my waistband. That was as high as I wanted the opening to go and, thankfully, turned out to be high enough to let the shirt lie flat on my body.
In this picture, you can see the finished stitching.
Repeat these steps on the other side and you're done.
As you can see, I wasn't too specific about lining up my old and new seams exactly. I tried, because I don't want the old seams to ravel, but when I took the shirt off the machine, I saw that I was slightly off. Did I rip out the seam or sew a new one to blend into the old seam? Of course not. I want some risk in my life. The risk of seams working themselves loose should do the trick.
You can also see that my stop-stitching is slightly angled. Do you care? I don't.
When I first started doing this alteration, I ripped out the seam to the height I wanted it, then sewed the seam allowance down in one continuous seam, back-tacking at the top before continuing down the other side. This produced a more pointed and bulky top to the opening because the seam allowance above the vent wasn't lying flat. So, since I didn't like the way it looked, I continued this process on several items. That's natural isn't it?
Today I realized I was missing a step in the process and making life difficult for myself. The five steps at the beginning of the article produce a more uniform, factory-like finish to your extended vent.