The Exposure Triangle
The basic building blocks of photography are the exposure triangle. That is Shutter Speed, Aperture, and ISO. Understanding how these three things work together is the first step to taking great photos. 
To take a properly exposed photo you need to let the proper amount of light into the camera. You do this by adjusting your settings for Shutter Speed, Aperture, and ISO. You can move these up or down to let more or less light get to the sensor. These adjustments are made in what we call stops. If you add a stop of light, you are letting twice as much light get to the sensor. If you take away a stop of light, you are letting half as much light get to the sensor. Let's look at how this works for the various settings.
Shutter Speed. This is how long the sensor is exposed to the light. So a setting of 1/200 means light is getting to the sensor for 1/200th of a second. In terms of stop, every time you double or halve the shutter speed, that is one stop. For example, if we go from 1/200 to 1/100 we have added one stop. Light is now hitting the sensor for twice as long, so the image gets brighter. Conversely, if we go from 1/200 to 1/400 we have taken away a stop. Light is hitting the sensor for half as long, so the image gets darker. The other thing to consider with shutter speed is motion blur. If you shutter speed is too low for a given subject, it might blur because of movement. The faster your shutter speed, the less chance for blurring. 
ISO. This is very similar to shutter speed. Every time you double or halve your ISO you are adding or subtracting a stop of light. The difference is the numbers work in the opposite direction. So as the numbers get bigger with ISO you are adding light. And as they get smaller, you are subtracting light. For example, if you go from ISO 1600 to ISO 3200 you have added a stop of light and the image will get brighter. And if you go from ISO 1600 to ISO 800 you have taken away a stop of light and the image will get darker. The other thing to consider with ISO is that in general the lower it is the better your picture quality will be. As you raise the ISO you are amplifying the signal going to the sensor and this will introduce noise. Your best picture quality will be at ISO 100. 
Aperture. This one is a little more complicated because it is not as simple as doubling or halving the number. The aperture scale looks like this:
F1, F1.4, F2, F2.8, F4, F5.6, F8, F11, F16, F22. 
It still works like shutter speed and aperture in that every time you move between those values you are doubling or halving the amount of light getting to the sensor. The lower your aperture number is the more light you are letting hit the sensor. For example, if you go from F5.6 to F4 you have double the amount of light getting to the sensor and the image gets brighter. And if you go from F5.6 to F8 you have halved the amount of light getting to the sensor and the image gets darker. The other consideration for aperture is depth of field. A smaller aperture number means that the area of the image in focus will be narrower. A larger aperture number means that the area of the image in focus will be larger. Think of a photo you have seen with the model in focus and the background blurred out. That is from a smaller aperture number. And a photo you have seen with most of the photo in focus is from a larger aperture number. The focal length of the lens and the distance to your subject also plays into depth of field, but we will cover that another time. 
Putting this all together. Now that you know how to add and subtract stops of light with shutter speed, aperture, and ISO you can start manipulating them in your photos. For example, let's say you are taking a photo and your settings are at 1/30, F8, ISO 400 to get the brightness you want. You might notice that 1/30 is too low because it has introduced some motion blur. You can trade stops from aperture or ISO to shutter speed. So, if we go from F8 to F5.6 we have added a stop of light to the photo. Now we can raise our shutter speed from 1/30 to 1/60, taking away a stop of light. Since we have added one stop and taken away one stop the brightness of the image will be the same. 
Another example. You are taking a photo and your settings are 1/1000, F4, and ISO 6400. The brightness you want is there, but you notice ISO 6400 has added noise to the photo. If there isn't a lot of movement in your photo, you can lower your shutter speed to add stops. If we go from 1/1000 to 1/250 we have added two stops of light. Now we can take away two stops with ISO going from 6400 to 1600 reducing the noise in the image. 
Experiment with your camera. Find a setting that works for a photo you want to take and then start trading stops to see how it works. Add a stop in one setting and then take away a stop in another. Once you understand this you can start to manipulate the settings to get the results you are looking for. If you want a blurry background, you know you have to trade stops to get your aperture as low as possible. If you are shooting something with a lot of movement you know you have to trade stops to raise your shutter speed. If you notice there is too much noise in your image you know you have to trade stops to lower your ISO. 
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