Rorschach Tests
Look at this picture. What do you see?

The answer is obviously Goro
Hermann Rorschach devised the technique of using random ink blots to probe the subconscious mind, based on the idea that patients would be prone to seeing images that were more important or relevant to their mental state. They would project their internal preoccupations onto the otherwise abstract shapes, revealing clues that could be deciphered by their psychiatrist.
The reason ink blot tests work is because humans are naturally adept at seeing images and patterns. Our brains are composed of an enormous collection of highly specialized neural circuits, custom-built for finding, storing and matching patterns. Parts of our brains are devoted to sensing contrasts, finding parallel lines, extrapolating three-dimensional depth, recognizing faces, anticipating motion — the list goes on and on. In fact, so much of our cognitive potential is tied up in neural pathways that are optimized for matching specific patterns, it is actually very difficult to avoid seeing them everywhere. In video game terms, you are almost all GPU with very little CPU. It is difficult for us to simply perceive information without our specialized capabilities biasing our interpretation of it.

Completely abstract shapes
This is great for surviving in the jungle, not so great for designing games. The problem is that we begin processing before we have all the information; we draw conclusions based on patterns that may not actually exist. Did that element dominate an encounter because of a fluke, or does it represent a trend? Is this feature a little out of tune, or does it hopelessly conflict with the rest of the game? It’s impossible to tell from a single example, but that doesn’t prevent us from making judgements based on one experience. And once we have a pattern in our head, Confirmation Bias kicks in and our brain optimizes further and starts rejecting data that doesn’t support our initial conclusion, making it even harder for us to be objective.
Confirmation Bias is especially potent for game designers, because we know what is supposed to happen. We wrote the paper design, we know how a mechanic was intended to constrain the gameplay, so we play our games as if the mechanics work properly — even when they don’t! We know the picture behind the ink blot, so we are incapable of seeing with unbiased eyes. Which is why we are so often shocked during playtests; what is obvious to us proves unintuitive and confusing without the pattern already in mind.
Unfiltered Perception
So train yourself to see the ink, not the pattern. Stubbornly stare until you don’t see an image, but only what is truly there. Then, when you play your game, divest yourself of preconceived notions of what the game ought to be and strive to experience the game as it truly is. This will allow you to see through the eyes of a new player.
Another method is to find Gestalt images, pictures that abruptly change meaning based on how you look at them, and practice switching between the competing interpretations. This will allow you to hold multiple explanations of the same game experience in your mind at the same time, so you can evaluate them all fairly.

Old woman, young woman, old woman, young woman...
It may sound ridiculous to spend time deconstructing smudges and turning old women into young women, but it will help reclaim some of those specialized circuits and increase your ability to process unfiltered reality. Which will make you a more effective game designer.