In any given photograph there are a number of elements which make up the subject which you are capturing. At times they are fixed relative to each other - for example you are photographing a rockface or graffiti on a wall - there is nothing to arrange. Your job in that case is to find the best angle to record the image and to frame it in the best way.
Often however, the various elements of the subject are not on a single plane and your camera position will affect how they relate to each other - overlapping, next to and just touching or near by. Through height of camera position you can affect the same issues vertically as you can horizontally by moving around.
In one camera position two objects can be equidistant, but as you move left or right, one is going to be closer than the other and their relative positions change, sometimes significantly. You have to decide what relationship works best for a given image. This can be relatively painless if there are only two separate objects in the image - say a tree and a rock, but becomes much more complex as the number of objects increase. In this case you find that while moving to the left will increase the spacing of one pair of objects, it narrows the gap between others.
How do you decide where to place all these objects relative to each other through camera position? What happens if this is a still life and you can physically pick up the objects and move them where you will? Are there rules that you can follow?
Before getting to what you should do, lets first contemplate what the significance is of relative position - perhaps that will give us clues as to what to do with them.
Remember too that while I write of "objects", they may in fact not be real, touchable, things. They might be a shadow or a highlight on the background.
At a most fundamental level, placement of the objects helps us understand the image. Since an image is two dimensional, placement helps us understand the relative positions of the objects. When one overlaps the other, it is clearly in front, while if they are next to each other, we don't know that. They might touch in the image but it doesn't mean they are next to each other. You may want to use this ambiguity to supply your viewer with a bit of a puzzle - something to wonder about, or you might prefer to make it clear where the objects are to enhance understanding.
Where the objects are located within the image has some bearing on how we interpret the image. We live on a planet surface and virtually all the time we can assume that what is at the bottom of what we look at is near, and the top far. As the photographer you have the possibility to confirm that or litereally turn it on it's head.
More subtly though, we tend to see bright objects as nearer, dark as further, large as near, small as far. To some degree you can filter or manipulate the image to lighten and darken objects in the editing to change that - for example two rocks of equal brightness could have one darkened and the other lightened and now there is a strong sensation of the light rock being nearer than the dark one.
Because of atmospherics however we also have the sensation that things that are light and soft and low in contrast appear very distant, while objects that are sharp contrasty and with a full range of tones including some good blacks are relatively near. This gives you the opportunity to use depth of field to give a sense of distance to objects - being out of focus and being light and with no good blacks would mean the object is assumed to be distant.
It is natural for the viewer to go from object to object as he or she looks at the image and the relative positions offers a chance for the photographer to tell a story or to introduce the main object or to explain it. The positions of the other objects will contribute significantly to how well that explanation, introduction or story comes across.
Fundamentally some arrangements are more attractive than others and create a visual path through the image, whether this is an S shaped path or the four corners of a rectangle or three of a triangle. "Placing" the objects in one of these patterns can give an image a sense of rightness, balance, peace or just the opposite.
Placing two objects next to each other in the image creates a connection between them, whether you wanted it or not, so you need to know if that is in fact what you want.
The more experienced the photographer, the more fine photographs that have been studied, the more images made, the better a photographer becomes at simply looking at the subject and knowing what seems right. Even after years however, it is often not obvious what is right and you actually do have to think about all of the above as you move around the scene trying to find the best viewpoint. For novice photographers it can be a nightmare trying to arrange things rightly. In fact novices often don't even know when they have done it wrong - or if they do, why, which can lead to a lot of frustration. The more levels you understand your images on, the better you can find your viewpoint.