Quite many know the joke about a typical DSLR user, who is only using full automatic settings and is getting worse photos than he wants to get.
You don't want to be one of those. However I know learning new things is really difficult, that's why I'm trying to explain the three big things in typical manual photography: Aperture, shutter speed and ISO (light sensitivity).
To help out, I'm giving different sets of photos and explaining which settings I'm using on the photos. I've seen similar sets on websites and in books, so I'm hoping they are the absolute best method to learn!
I've learned these things in Finnish, so if anyone notices I'm using wrong terms in English, please point it out to me!
Aperture
In the photos below I'm using shutter speed of 1/100 and ISO 100.
You can see effects of different apertures, when shutter speed and iso are staying the same. The smaller the aperture number is, the brighter the image is, as the camera sensor is getting more light from the larger aperture.
Aperture: f/1.8
Aperture: f/7.1
Aperture: f/13
You can see how aperture affects the amount of lights in the photo. All lenses are not capable of having as great aperture as others, as typical lenses have maximum aperture of f/4.5 or f/3.5, meaning you can't go as far as f/1.8 or further. Some lenses can reach aperture of f/1.2 or f/1.4, which are extremely good for low light conditions (or to get a nice bokeh).
Why use small aperture, if the image gets darker?
Most importantly, because aperture affects the how shallow or deep the focus is on the photo!
Let's see below:
f/1.8 (ISO 100, shutter 1/500)
f/7.1 (ISO 100, shutter 1/25)
f/22 (ISO 100, shutter 1/5)
You can see how I had to adjust the shutter speed from 1/500 of a second to 1/5 with the smallest aperture to get the image bright. However, what's important you can see the difference in depth of view.
In first image, background is blurry but in the last one, it's sharp even to the neighbors balcony.
At worst, using a large aperture in a portrait photo can cause camera to focus on the tip of the nose, leaving rest of the face blurry.
ISO
In the photos below I'm using shutter speed of 1/100 and aperture of f/3.5.
ISO is basically light sensitivity. The higher the ISO value is, the more sensitive the camera sensor is to light. By increasing ISO value, you can get more light in dark conditions, just in case you do not want to use large aperture and/or slow shutter speed.
ISO 100
ISO 400
ISO 1600
You can see how the image is becoming brighter and brighter without adjusting other values. ISO helps especially in dark conditions and when you need to have large depth of focus and/or fast shutter speed.
However, the issue with light sensitivity is that the sensor is also getting the "bad signals" more easily, causing disturbance on the sensor. This can be seen as "noise" in the image, lowering the image quality.
The smaller the camera sensor is, the worse it can handle higher ISO values. This is one special reason for full frame cameras, as they have large sensors. Phone cameras typically have small sensors, which cause them to be terrible at photography in the dark.
ISO 25600 (Shutter speed 1/4000, f/5.6)
The photo above is with extremely high ISO value. I've cropped a small piece of the photo below:
The image on the left is ISO 25600, the image on right is ISO 100.
The quality is OK even with ISO 25600, but you should be able to see the difference. If you don't, it's fine too :)
Shutter speed
Images below are taken with f/2.5 and ISO 400.
Shutter speed reflects how fast the camera shutter is. It opens and closes, letting light in and then the image is born.
Well done.
The faster the shutter is, the less light can enter. However if the shutter speed is slow, you get more light but all movements cause the image to become blurry. The model is moving a bit, your hand is shaking, wind is making grass wave...
1/125
1/15
1/4
You can see the images are getting more and more light, but the movement is getting blurrier. Sometimes the blurriness is something we want to achieve, but not always.
To get movement really to stop, you need really fast shutter speed. I usually get disappointed when a photo seems OK on the small camera screen, but isn't sharp in the end and I've used too slow shutter speed for most of my photos.
1/1600, ISO 2500, f/2.2
3.2, ISO 50, f/20
Yes, instead of 1/something seconds I used shutter speed of 3.2 seconds. To get this photo, I used a timer and a tripod.
As you can see, I managed to get a real nice effect using a slow shutter speed, but I'm also real happy about the photo above as the movement seems truly stopped.
Conclusion
Most cameras have automatic or "semi-automatic" selections. Some allow you to pick ISO and letting the camera to calculate other values - or you can choose ISO and aperture/ISO and shutter speed, leaving the camera to calculate required value of shutter speed/aperture for the optimal photo.
That's how I started and I moved on to using manual selections. The thing is, you usually have to be changing all the values if the conditions are changing or you're taking different kinds of photos.
Be brave to push yourself onto new levels in photography, but don't take stress in going straight to the top.