This applies to software design, project design, and software test. The more simple it can be and still solve the problem, the better off you are. If you can write a test with 16 steps to show a bug, or a test with 4 steps to show the same bug, go with the four-step test. If you can put together a project plan on the wiki you already use or you can go buy project management software and learn it, go for the wiki.
Make it easy. Make it work. That is simplicity.
When things stop working it's generally fairly obvious. Something will break, or in the case of human processes, something will start to feel wrong. Functionality is a prerequisite; if it has to be more complex to work, then it has to be more complex.
Once it works, though, making it as simple as possible is the goal. It's hard to do, and it's scary to decide to skip something or to not do something. But as long as it works, ask yourself if you can do it more easily or with fewer steps.
It's hard but possible to be simple enough to obviously work. Let's see how close we can get.