What are the main functions on a DSLR camera that affect the correct the exposure of an image?

Context: In photography, exposure value is a number that represents a combination of a camera's shutter speed and f-number, such that all combinations that yield the same exposure have the same EV. Exposure value is also used to indicate an interval on the photographic exposure scale, with a difference of 1 EV corresponding to a standard power-of-2 exposure step, commonly referred to as a stop.

The EV concept was developed by the German shutter manufacturer Friedrich Deckel in the 1950s. Its intent was to simplify choosing among equivalent camera exposure settings by replacing combinations of shutter speed and f-number with a single number. On some lenses with leaf shutters, the process was further simplified by allowing the shutter and aperture controls to be linked such that, when one was changed, the other was automatically adjusted to maintain the same exposure. This was especially helpful to beginners with limited understanding of the effects of shutter speed and aperture and the relationship between them. But it was also useful for experienced photographers who might choose a shutter speed to stop motion or an f-number for depth of field, because it allowed for faster adjustment—without the need for mental calculations—and reduced the chance of error when making the adjustment.

Answer: If a DSLR camera is not set to 'Automatic' mode, there are 3 primary functions that need to be considered when deciding on the correct exposure for your image.
1) the Aperture - how wide the aperture on the lens is set determines how much light can pass through the aperture. A small aperture (e.g. f/16) allows less light to reach the sensor as opposed to a wide aperture (e.g f/2.4).
2) the Shutter Speed - how long the shutter is allowed to remain open after you depress the release on the camera. A short exposure time (e.g. 1/1000 sec) will allow less light to hit the cameras sensor whilst a long exposure (e.g. 1/4 sec) will let more light hit the sensor
3) the ISO setting - this setting is used to control how sensitive the sensor is to light hitting it. A low ISO setting (e.g. ISO 200) is much less sensitive than a high ISO setting (e.g. ISO 1600) which means less light is required to capture the for the image on the sensor.
All 3 of these functions work in tandem to ensure the correct exposure value is created based on the image and effect you are trying to create.