Here are the cliff-notes: If the sun is out (not overcast) shoot only in full shade (no light is streaming thorough) OR expose for only the light and shoot things that are only in that light...therfore letting the shadows go black. If it is overcast (great!) shoot all you want but don’t include the sky, because it will be all white.
Let’s talk about the sun. To the camera, the sun is very bright, brighter by 3 times as much light than the shade (sometimes more if there is a lot of cover) and this is beyond the range of our cameras. Therefore, we can expose only for the sun or only for the shade. Not both. Here are 3 shots of the same scene: exposed for sun, exposed for shade and then "exposed for both."
Sure, the bottom shot will work in a pinch but it is not worth printing, so just accept it and embrace it like a silly uncle. Use manual exposure or Exposure Compensation (your most important button) to tell your camera which one to expose for. I usually try to avoid exposing for the shade (although it can sometimes work, especially if there are people in the shade) because when you have a lot of bright spots on your photo it looks funny…and our eyes tend to be drawn to the brightest parts of the scene.
Now here is the takeaway: look for subjects that are only in the sun (or wait for them to walk into it) expose for them and see how your images pop!! Letting the shade go black creates drama and can sometimes hide the clutter of a complicated scene. Once you get this idea down start taking risks (risk can sometimes yield good photos) and be adventurous: start looking into the these shafts of light and see what you can create.
But what about those days that are both? These are great because you get the best of both worlds...if you are patient. A side effect of paying attention to light is that you will learn to be aware of changing light levels. Like on days that clouds are moving, shading the sun for a bit and then not. Below is an image I was waiting for because the clouds were shading the scene, but I knew it would leave soon. I watched as several photographers came to take a similar shot when the clouds were blocking the sun. I saw them look at their images, take more, look at their images, and shake their heads. As soon as the sun peaked through to light up the subject with great light I took two frames and I looked around for the other photographers...they were off down the street looking for their next snapshot. They were not paying attention to the most important element in photography: light.
What about HDR? Well, if you are an HDR monkey and into that kinda thing, then sure, that is a way to take photos in contrast situations because you can use your computers to make it look "cool." I will not say that this is silly, or that there may be a time and place for it, or that some people over use it...no I will not say that at all. And no, I am not going to tell you how, because I have never done it. If you want to know, there are way to many tutorials online. But because you asked, this is my first...and so far only 'HDR' image. (by the way, it was faked: I didn't take multiple images or use an HDR program, it was one image...just heavily stylized in Lightroom.)
So there you have it. No matter what light you find yourself in, learn to utilize its strengths. But also remember that ugly light is unfixable, I am talking about harsh overhead light that is usually found between 10:00am and 4:00pm. So get up early or eat dinner late to take advantage of the great low light, and then learn to enjoy your surroundings when photogrpahy is not working...because your eyes (and your soul) can still enjoy nature, even when your camera can't.