A lot can be changed with these simple rules to follow.
Outdoor lighting can be amazing or terrible. It all depends on the angle. Indirect light is always the most pleasing to the eye. Harsh sunlight can really affect the softness of someone's face.

If you are in a park, for example, and it's 1 in the afternoon, the sun WILL be high in the sky shining down and all over your face. This creates harsh shadows on your clothes, under your eyes, around your cheeks, etc. It is very unflattering light.
Instead of shooting facing the sun, or shooting below the sun, find a tree that is casting a large shadow. Find a wall that blocks the sun's harsh light. Put yourself against the sunlight. Anything you can do to put more focus on your subject matter, and less focus on how bright it is!
With that in mind, I move onto backlit pictures. There is a time of day, some people call it the golden hour, near dawn or dusk when the sun is lowest in the sky. Sometimes this gives the world a slight golden glow, sometimes, a blue glow, etc. It depends on the weather that day, but in general, it is ALWAYS the best time to take someone's pictures. This is a time when photographing someone looking into the sun is more plausible (because the sun is less intense). Photographing someone against the sun, however, is your best bet. The light is more forgiving on faces. It creates a vintage/foggy effect on your subject, and overall, sets a perfect tone for your picture. Instead of heading out for some pictures at 11 in the morning, try 4 or 5 (depending on the time of the year). Your results will be far more stunning!
Natural light is ALWAYS better. Whenever you can, take your pictures outside. Indoor lighting can leave your images looking orange and grainy/blurry.
If you are having orange toned pictures a LOT, there are two ways to solve it. First, your indoor pictures are probably being taken around yellow lamps that are giving off a warm tone to an already warm toned picture. If this is the case, it requires changing your white balance on an SLR camera. If you are NOT using an SLR camera, you must do other things. Open some windows! Let that natural light in! Second, you can edit your colors very easily in photoshop. Want to learn more about color adjusting? Click
here for a quick tutorial!
The Rule of thirds is a pretty basic rule to follow. As most people do, we center our subject matter in the middle of the frame when taking a picture. But is this always the best way? DEFINITELY not always. Moving your subject to the sides of your image can really bring a whole new dimension and grasp someone's eye quicker. Shots taken straight in the center can be uninteresting, boring and pretty simple. I move my subject matter to the side a bit and I bring out a whole new feel to the image. Make sure that whatever your subject matter is, that they are facing inward to the picture. For example, do not have your model stand to the left of the frame looking off to the left. This leads our eye OUT of the picture. Make sure their face is turned to the right. That way our eye stays inside of the image frame where it belongs!

Centered, straight forward portraits work for dramatic shots. Not for nice smiling pictures in most cases. A center portrait is what most people would do! You're not most people and the only time that I see center, straight forward shots of a single person working really well, is when there is a unique angle or when your subject matter is serious.

Get down low to take a picture of an object or person and then compare to taking one standing up.
Look down at a person and then take one looking forward at them.

See the difference? It's a little more interesting, sometimes more flattering and immediately grabs our attention more because it is different from the normal posing you would see!
Don't be afraid to crop. Take a picture of someone making a funny face with all of their face in the frame and then one where it's cropped right below their nose. Just like before with moving your angle, moving your crop is something to play with. People don't have to see the whole image. Sometimes having a tiny view into an image is just as exciting!
Avoid direct flash at all costs. Always, always, always, open windows, doors, blinds, curtains, anything to let more natural light in BEFORE you settle with a flash. If you use a point and shoot camera and have no way around using the flash indoors for something, try covering the flash with a piece of white paper as you take the picture. This lessens the intensity of the flash and distributes the light a bit more! Never use flash outside. If your camera always flashes, cover it up! Natural light is always more pleasing to the eye!

Which one looks more natural? Do you see all of the harsh shadows and shine the flash gives?
Set up a backdrop for a still life shot. Get rid of distractions for portraits. Instead of taking your outfit picture in front of the big screen tv, take it in front of the brick siding of your house. Instead of photographing your cute cat next to a stack of magazines and dvds, spread out a blanket to surround them. Remember that you are taking a picture of ____ and no one/thing else. You don't want a tissue box behind your pretty DIY finished work. You don't want your boyfriend's moped sticking half way out into a shot of you in a pretty dress! No, no, you want to keep the focus on your subject. Background objects can ruin that. As you may notice, however, I use an SLR camera which allows me to blur my background. This helps if there are a lot of background distractions, but it is still an important rule to follow, regardless!

Hopefully this was helpful! There are some exceptions to these rules, but the most important thing to remember when taking pictures is to be observant. When you look at other people's photographs, observe what you like about them. Try to notice the things you wouldn't normally notice. Angle, lighting, colors, background, posing, movement, etc. etc. etc. If you become more and more aware of what you love when you see a photograph, then you will apply those same principles to your own photos!