Exposing correctly in photography is not rocket science, but you should not let your meter choose your settings all the time. It will work fine in normal situations, but fail when you want to get interesting light. Here is a guide to make things simpler.
Camera meters always meter for a middle tone of grey. It's the photographer's duty to know where they want their blacks and whites.
Most people think that modern cameras, with their advanced metering systems, able to analyze 60 areas of the framed subject, are foolproof when it comes to exposure.
Let me say this as gently as I can: it does not always work that way. All cameras, whether it's a top professional DSLR or a simple compact camera, measure light the same way: they all try to represent the scene in front of them as a middle grey card. A 18% grey reflectance card, to be more precise.
When people point and shoot and expect to get good pictures, they usually get them. This happens because most scenes have a mixture of darker and brighter elements that average to a middle grey tone, so everything seems to be in place.
But when you deviate from normal light situations, where there is too much light or dark, and you still just point and shoot with your camera, you do not get the image you want.
I've tried to explain this to people at my workshops, and the best way I found is to use two pieces of card, one white and the other black, and show them what happens when I photograph each of them. I think this is the easiest way to make people understand how the reflective light meter in their cameras work and the measures they have to take to get the proper exposure.
The result when you let the camera choose exposure to photograph a white card is... grey.
1. Exposing for White
So, follow me on this experience. Use a place where light is constant, so you can keep the same conditions for each shot. First set your camera to Program or any mode that automatically defines exposure. Now get a white card in front of the lens, so it fills the frame and press the shutter to get your image. It does not matter if you cannot focus on the card, just disable AF and focus by hand.
If you look at the results on your camera's screen you'll find that what you got is a muddish gray representation of the white card. It can have a slight color tone depending on the ambient light you're working in, but it's surely not white. No, there's nothing wrong with your camera or your eyes. The meter in the camera is simply doing what it does best: to represent the world in the middle grey it knows well.
And if you change the white for a black card and let the camera choose, it gives you a nice shade of... grey!
2. Exposing for Black
For the second photo keep the camera in Program as before but change the white card for a black card, exposing it in the exact same conditions. If you look at the image on the screen you'll be tempted to think you're still looking at your first photo. It looks grey. Yes, the camera did not understand what you wanted to photograph and just did what it knows best: change everything to middle grey.
3. Correcting exposure
Now that we have confirmation that the camera meter does not know the difference between black and white it's easy to understand what we have to do to correct the exposure when we're faced with subjects that are lighter and darker.
The rule is simple: when you're photographing subjects with lots of dark tones, you'll have to compensate, giving it less exposure than the meter asks for. That compensation can go from 1/2 stop to 2 stops, depending on how dark you want your subject.
If you're photographing light subjects, you have to compensate exposure in the other direction, opening 1/2 to 2 stops. This can be done by either changing aperture or speed, depending on the results you're looking for, or the mechanical limitations of your system.
I think that what usually confuses people is that with dark subjects they tend to give more exposure, when less is the correct answer. And with white subjects you need to give more exposure to get proper whites. As a guide (and not a rule) remember that to get proper blacks you'll need somewhere about 2 stops less light, while for bright subjects you need up to 2 stops more light. This means that a "proper exposure" will always have a tonal range that covers about 5 stops - 2 on each side - from the medium grey point the meter chooses.
Get yourself two pieces of card, one white the other black, and try this at home. You'll find that you always get tones of grey if you let the camera decide everything. And this happens under different light conditions.
Once you get a black card besides a white card, the exposure meter in the camera will give a good representation of both.
4. Final Test
Now to get us back to the beginning, place the two cards side by side. Use the Program on the camera, meter from the line where black and white join and look at the result: perfect Black and White. If you want to experiment further, move the cards slightly so there is more black or white covered (75% to 25%, for example) by the camera meter and see how the representation of the white and black change. Simple, isn't it?
If you remember this little experiment your exposures, from now on, will be better. Try to understand what are the dominant tones in the framed subject and adjust the meter accordingly. That's what I teach my students. It's very much like seeing the world in black and white.