In short, sharpening planer and jointer blades is more difficult than it looks, and is probably not worth it. Get them sharpened or buy replacements if you value your time. I originally was inspired by this article:
I built a similar jig that looked like this:
I had used the sandpaper-on-glass technique for other projects, so I felt it could work well for sharpening knives. It works, but it's SLOW. My knives were in admittedly bad shape (very bad shape -- see picture) and needed a lot of material removed. I resorted to using a power sander to take off the initial material. Also my jig is not as good as the one shown in the link because tightening the screws will make the jig not be perfectly straight anymore.
Before and after
Yeah, it's sharp! The blades appear to be bi-metallic. I am not sure if all planer blades are like this, but there are definitely two different types of steels joined together.