We can't imagine digital reflex cameras without optical viewfinder because it displays the subject in real time and unaltered. This kind of targeting is proven especially at strong sunlight and also for focusing and is often preferred compared to the electronic variant.
Viewfinder in DSLR cameras
DSLR camera have a reflective oscillating mirror to enable displaying the subject in the optical viewfinder. The mirror is located, depending on whether the viewfinder or the Live View mode is used, in a different position and therefore can redirect the light information inside the camera, respectively let it pass through to the sensor.
How does the image appear in the viewfinder?
In order to capture the subject through the ocular, the mirror is placed in-between the light path of lens and sensor and it reflects the incoming light up to a focusing screen. The motive that is projected on the screen is mirror-inverted and is redirected by a further lens element to a prism. Now this reflects the light information so that the motive can be viewed in correct way – prism viewfinder.
Instead of a glass prism some DSLR cameras use a so-called pentamirror. This also ensures an unreversed representation of the subject. However, the light is redirected to the ocular in a different way. Other than the prism, the pentamirror has a mirrored surface for directing the light to the viewer.
How big does the viewfinder display the image?
The size of the viewfinder image is directly related to the frame coverage and the magnification. For a better understanding, we take a look at both aspects separately first.
The frame coverage describes how many percent of the image captured by the sensor will be displayed in the viewfinder. A specification of 100 % frame coverage means that the photographer sees exactly the same section that will be captured in the final image. But many DSLR cameras only offer a frame coverage between 95 % and 98 %. In this case the subject will not be fully displayed in the viewfinder, but cropped. This means that the edge area of the scene will not be visible in the viewfinder, but will be captured in the final image. As a result it can happen that elements photographers want to exclude from their composition, unintentionally become visible in the image.

Even though the frame coverage does not include any information about the actual size of the viewfinder image, it is affected by it. For a better comprehension we take a look at the magnification. This delivers important information about how large the subject will be displayed in the viewfinder. In other words: If the image in the viewfinder will appear larger or smaller compared to viewing it with the bare eye. In the technical specifications you will often find values below 1, indicating that the image size in the viewfinder is reduced. Therefore, when looking through the viewfinder with one eye and looking at the scene with the other eye, the image in the viewfinder will appear the same size when the magnification is 1. For values below 1 the viewfinder image will appear smaller.
The connection between frame coverage and magnification
Two screens with the same magnification do not necessarily display the subject in the same size. A different frame coverage with the same projection area affects the size of the viewfinder image. When comparing 100 % frame coverage (illustration on the left) to 95 % frame coverage (illustration on the right) of the same area, the cropped image seems larger. Vice versa a different frame coverage and a different magnification can lead to the same viewfinder image size.
Does this mean that you have the same viewfinder image size when magnification and frame coverage are identical or when their combination leads to the same result? No, because the magnification has to be considered in relation to the sensor size.
Magnification versus sensor size
Basically it applies, the higher the magnification value, the bigger the image is represented in the viewfinder. But this is not always the case because also smaller values can lead to a bigger image display. With 100 % frame coverage the motive can seem smaller with a magnification value of 0.85 than with one of 0.72, for example. This sounds odd, but can be explained by the sensor size. The specification of the magnification typically is related to a 50 mm lens (focused at infinity). With a camera whose sensor is smaller than full frame, the stated magnification relates to the use of a 50 mm lens, thus a 35 mm equivalent focal length.
When comparing viewfinder image sizes, you should keep the connection between magnification, sensor size and frame coverage in mind. Take a look at the technical data of your camera to find out what frame coverage and magnification your viewfinder offers. This way you can determine your image composition.
Diopter adjustment
If photographers wear glasses, the distance between eye and ocular expands and additional space arises to the eyecup. Thereby, the observer may not see the whole viewfinder image and ambient light can disturb the viewing and / or focusing.
Because of this most cameras have a diopter adjustment. With that, the viewfinder can be adopted to a short- or nearsightedness by an additional little dial at the side of the ocular. So, glasses become dispensable within a certain diopter range and the motive can be captured with the unaided eye. The compensation values vary with manufacturer and model and lie often between +/- 3 diopters.
Black viewfinder image
There are two reasons why a black image appears while looking through the viewfinder. The matter of the first case is the releasing of the camera while using the viewfinder mode. If you look through the finder during the release, the sight will be interrupted for a brief moment due to the oscillating mirror. To enable the light reaching the sensor during shutter release, the mirror is flipped up. Nearly simultaneously the shutter is opened and the sensor can capture the motive. With the raised mirror the light information is not directed to the viewfinder, which in turn appears black – as long as the exposure lasts. If the image is taken, the shutter closes, the mirror switches back down and directs the image to the viewfinder again.
The second case, where the viewfinder appears black, shows while using the Live View mode. If it is active, the display serves for viewing. Thus the monitor can display the subject, the mirror is flipped up and the shutter is opened. By this the light path is released to the sensor and the light information can be processed for viewing. Meanwhile the light flow to the viewfinder is interrupted and therefore only shows a black image in the viewfinder.
But also the monitor can temporarily appear black. Why? While releasing in the Live View mode the shutter has to be closed, so it can be opened and closed again for capturing the light information. And in this period, the monitor shortly appears black.
Optical viewfinder camera
Some compact cameras contain another, simpler optical viewfinder type or can be equipped with those. Using typical optical components, these direct viewfinder give back the motive to the photographer by an eyepiece. If the viewfinder is integrated in the camera, it is mostly located beside the lens and allows a direct look at a subject. Thus, the image is not displayed by the light that is passing through the lens. For this reason the displayed image is not affected by focal length adjustments and remains the same in the viewfinder.
Illustration of viewfinder sights:
Whether wide-angle or telephoto, the viewfinder image of a direct optical viewfinder (illustration on the left) remains the same. With a prism viewfinder, however, the light information that passes through the lens is displayed. By this the view changes depending on the selected focal length (illustration in the middle and on the right).
Bright frame
Solutions for determining the image crop at different focal lengths are provided by bright frame viewfinder, for example. Here, a bright frame is used, which usually represents the recording range of two focal lengths by existing lines.
Parallax
In some cases, also a parallax compensation is given / considered. But why and what is the parallax? Since optics and viewfinders do not form a common line, the viewed motive display differs from that of the recorded image. In other words, through the side-shifted viewfinder, the photographer and the camera have two different viewing positions. As a result two light paths, thus two different motive sections, arise. A shift in the perceived subject occurs – parallax.

Rangefinder
Another optical viewfinder type is the rangefinder. Here, photographers cannot only view the motive, but also focus on it. Besides the simple viewfinder window, rangefinder cameras have a second window for distance measurement.
The concept: The light information that arrives at the rangefinder window is passed on to the viewfinder and thus to the observer. A semi-transparent mirror, which is located in the viewfinder area, enables the information passing through to the viewfinder. In the viewfinder, both images are now displayed in a specific area. If the subject is out of focus, the image sections are overlaid or shifted to each other. If the subject is in focus, the viewer sees a coincide image.
There are two methods for focusing:
1) Double image method
In this method, the two images (viewfinder and rangefinder) are displayed on top of each other.
If they are shifted to each other and duplications occur - the subject is not in focus (illustration on the left). By changing the distance setting of the lens, the corresponding image section of the rangefinder also shifts. The motive is in focus when both images are superimposed and no duplication occurs (illustration on the right).
2) Split image method
In this variant the two images are displayed separately from each other in a segment of the viewfinder. The first image is shown in the upper half and the second image in the lower half.
Looking at the branch of the left sample, it seems dissected and shifted against each other. As long as the upper and the lower split images do not built one uniform image (illustration on the right), the subject is not in focus.
References: https://de.wikipedia.org/wiki/Sucher_(Optik) incl. links, https://de.wikipedia.org/wiki/Entfernungsmesser_(Kamera) & Leica M Instruction