HDR (High Dynamic Range) photography is a technique used to capture the tonal range of a subject (light/shadows), yielding more detail in the picture. There are a lot of ways to take HDR pictures, but here's a quick and simple way to make a HDR picture without the hassle of thinking too much. You can also try this out on a point and shoot camera if it has a shutter speed setting.
So first things first. The whole process would be a lot easier if you have a tripod so that in post process or in camera process (if you prefer -_-) the multiple exposures line up perfectly without any ghosting. Also, be sure to NOT change your aperture or iso throughout the process, otherwise some pictures might come out sharper than the others, or more grainier than the others. Anyways, you're going to take more than one exposure in order to get the tonal range of the picture. Start off by taking a normal balanced exposure to get your middle tones. This was shot at 1/80s F/2 iso 200
The next step is to take a overexposed picture by slowing down your shutter in order to get the shadows of the subject/surroundings. Shot at 1/3s F/2 iso 200
After your overexposed picture, the last thing you'll need to cover is the Highlight/light range. For this, you're going to speed up your shutter in order to get the bright parts of your subject. Keep in mind you don't want to set your shutter speed too fast, otherwise you'll end up with a picture that looks like it was taken with your lens cap on. Shot at 1/100 F/2 iso 200
You're next step is either to combine all your exposures in your camera, or combine them using post processing software, such as photoshop. I chose photoshop because it obviously gives you more options to adjust the exposures individually. Take your time in post processing, don't think that just because you can add a lot of effects, it will fix your errors. Here's is the end result.
You can see the detail in the tonal range from lights to shadows. Obviously this wasn't a very contrasty scene to begin with, but the end result comes out more detailed than a balanced exposure. Again, there are a lot of ways to do HDR photography so don't think that this is the primary way, everyone finds their own method. A good note that I found out is that the more exposures you have (ranging from little changes in the tonal range), the more detailed your end result will be, but be sure to look at your scene, the more contrast in light/shadow, the better HDR effect you'll see in the end.