There is a particularly relevant video from the this old house archive:
Also, many portable air conditioners come with a fitting that is designed for through the wall installation. Remember to find some sort of flap type opening (like those on many dryer vents) that will prevent hot air and other debris from entering your portable air conditioner.
It's worth noting that portable AC window kits are often designed for windows that open both horizontally and vertically so you might be able to save yourself a lot of time and hassle by not cutting a hole in your wall. Here's an installation video so you can get an idea of how they vent through a window: