Simplicity can be Complicated
It is often said that one of the best ways to improve an image is to simplify it. But achieving simplicity can be complicated indeed.
Here's a typical scenario. You're out with your camera gear and you come across something that looks interesting and likely to make a good photographic subject. You point your camera and shoot. But the frame of the camera is unforgiving. Whereas the human visual system tends to focus on what it finds of interest, automatically paying less attention to everything else, a camera records everything it sees equally. It's not uncommon to take a series of images only to notice after the fact that every one has the same defect that you never noticed while shooting. Only when the task at hand has concluded do you truly find out what you ended up with.
It's not easy seeing as the camera sees. You went looking for something to take pictures of and you found it. It's only natural that you pay most of your attention to what you've found. The frame of a camera may be a perfect rectangle, but it's almost as if the frame of your vision adapts to the shape of your subject, regardless of what it may be. See a mountain and your vision is mountain-shaped. See a tree, and it becomes shaped like a tree. After all, why would we pay attention to what isn't of interest.
It can take a conscious effort to examine the entire frame before you shoot. You have to pay attention to both subject and background. And to do that, you have to be fully in tune and aware of what your subject is. Specifically.
That subject may be a particular object, or it may simply be a shape or a color or a mood. But you need to be precise. Personally, I tend to focus less on what something actually is and more on what something evokes or seems like. I find that if I can be less literal in my assessment of the subject, the more quickly I can get to simplicity. Get too specific with a literal interpretation and I can fall victim to the tendency to include too much. I want to contextualize it. But if I stick with impressions and stay more subjective, my subject has no actual context. It's automatically simpler.
Spend some time with your subject. Get acquainted with it. In so doing, you may find that your idea of that subject gets narrowed as you weed out details not strictly relevant, causing your choice of subjects to become ever more simplified. You'll know when you've started to reach optimal simplicity when you notice that further simplification gradually transitions to further clarity. As you gain a clearer sense of your subject, you'll learn which attributes to stress in your composition. Getting closer can often improve simplicity, but this results mainly from the forced simplification of the zoom lens as opposed to any well considered observation. Try it to see if it helps, but don't feel locked into the idea that closer is always simpler.
Try to pre-visualize exactly what you want your final image to look like. All the normal rules and guidelines of composition are just as relevant regardless of how much you simplify. Every aspect of your image should be a matter of choice. An image with a simple subject bulls-eyed in the center of the frame is a very different thing from an image of that same subject placed at an intersection of two thirds lines.
Lens choice and other technical decisions should be brought to made in service of your pre-visualized simplicity. If you need a particular shooting position and distance, a particular lens or shutter speed, take the time to set up what you need and make it happen.
Some writers have suggested simplifying your equipment as an aid to simplifying your images. That may seem like a good idea since you'd thereby end up with fewer choices and decisions to make, but I can't really agree with that. The goal really shouldn't be fewer decisions. It should be simpler images, and if that means I need a particular lens, it won't do me any good at all if I only brought a different one with me. I'm not looking for images that are simple to make. I want images that are aesthetically pleasing because of their simplicity.
You'll want your camera set on manual exposure too. Your camera may be able to determine a satisfactory exposure when set on fully automatic, but why deprive yourself of full control over not only exposure, but aperture and shutter speed as well.
Although it is generally advantageous to well understand your subject before you shoot, simplicity can sometimes be achieved instinctually. Sometimes a composition and a subject can just feel right, and so you go with it. Think of this as somewhat the "free jazz" approach to composition. I'll do this myself as a starting point sometimes if an idea strikes me right off. But I've found that further refinement can sometimes improve things even more, either through greater simplification or through reinforcement of just what attributes best convey that simplicity. If you realize your starting to over-think things, you can always return to your original inspiration and go with that.
Weeks, months, or even years later, it's not all that uncommon to look at what you've shot and realize you could have refined your concept even further. Simplicity isn't a specific goal post or horseshoe stake that earns you points if you can hit it. It's more a direction to aim for. More can always be achieved.