Following are the steps that you can take without disassembling the keyboard. We will be opening up the shell of the keyboard anyhow for our project, but its a good idea to clean what we can first so that debris does not make its way into parts of the keyboard that previous were protected. These steps are also good to perform every so often to take of any grime from normal use.
Some have one-piece integrated key caps - mostly later models, models that were branded for other companies (such as Lexmark and Dell), and the "quiet touch" (rubber dome) models. If your Model M has one-piece keys, you might find it easier to remove them by prying them off as shown in the next step.
If you look closely at the photo, the spring that was under the "grave" key (`) is caught on the barrel. That's not uncommon, so take a moment to look for anything like that and straighten it out.
This particular keyboard has a lot of crud on the barrel frame so I'm going to go over it quickly with a vacuum before I do anything else.
The Model M's keys are made of durable PBT plastic and the legends are applied via dye sublimation, so cleaning them like this should not cause any damage or fading.
Pro tip: Apparently the previous owner didn't like the Page Up key or something, and put an X on it with permanent marker that didn't come off in the wash. I was able to remove it by applying some alcohol-based hand sanitizer and letting it soak for a while, followed by light scrubbing.
In order to remove the keyboard's shell, continue to the next page about disassembly of the Model M. It is a bit easier clean the shell and the barrel frame when the keyboard is taken apart, so if you are going to take it apart anyhow you might as well wait until it is in pieces before you do that.