Elements & Principles

In art and design there are "elements" and "principles".  Elements are the "stuff" of your art and the principles are how you put that "stuff" together to make a composition.  These need to be understood and used to create a good composition.  The elements I like to focus on are Line, Shape& Form, Texture, Value & Color.  I have found many lists of different principles over the years, basically the same, but some use different words that mean the same thing to me.   So here's my list:  Space, Emphasis, Rhythm/Repetition, Contrast/Variety, Balance, & Proportion.  Some people add Unity and Harmony but I think if you have all of the others you will have unity and harmony. 
For the independent artist capable of understanding these concepts they can be a sort of check list to check your art and make sure it is meeting the criteria.  If something doesn't seem quite right, probably one of the areas mentioned needs work.

Elements

Line
Line is the beginning (I love lines).  There are angled lines, curved lines, horizontal lines (left to right- think horizon), and vertical lines (up and down).

Shape
There are basically two categories of shapes.  Geometric and Free-form.  They are exactly what they sound like.  Geometric would be your shapes with names like circle, triangle, square, rectangle, etc.  Free form is more like lava lamp shapes or even a silhouette.  Every complex object can be broken down or simplified into basic geometric shapes. 

Form
Form is giving the shape it's third dimension so it is no longer just a flat shape

Texture
Texture is smooth, rough, soft, hard etc.  I find the best way for me to get a texture across in a flat surface or drawing is to look at the light and shadows on the object and draw the shapes of the shadows.

Value
Value is the gradual change of light to dark.  The basic parts of value are a highlight, shadow core, reflected light, and the cast shadow. Value is affected by the shape of an object.  Spheres, cylinders, cones, and cubes are the basics.  Once again, breaking down complex objects into basic shapes/forms is important.

Color
The color wheel.  Every time I do a lesson or painting class using color with students we do a color wheel.  I remember thinking "another color wheel?" in every art class I took all through high school and college classes and the interior design tech school classes.  Always a color wheel.  Red, yellow, and blue are the primary colors.  Red and yellow make orange, red and blue make purple, yellow and blue make green; the secondary colors.  We know that already, right?  Well, the reason I do it again with every lesson is simply different mediums mix differently.  For example if we are using watercolors it is a great way to test the paints and see the way this set of paints mixes to create colors.  Using acrylics is different than watercolors, using colored pencils is different than paint, and crayons, pastels, markers, they all work differently.  Experimenting with them in a color wheel is great way to get to know your medium.
Some vocabulary going with color are:
Hue=the pure color you are starting with.
Tint= hue + white. Tone=hue + gray.  Shade=hue + black.
Monochromatic color scheme= one color, it's tint, tone, shade and black and white.
Complementary color scheme= two colors opposite in the color wheel.
Triad color scheme= three colors equal distance on the color wheel.
(there are more color schemes, but those are the very basic)

Principles

Space
There is positive space and there is negative space.  The positive space is the object itself and the negative space is the area around it.  Think of a white sheet and shadow puppets.  If you had a vase behind the sheet it would make a black silhouette vase shape.  That black shape would be the positive space and the white would be the negative space.  If you had a chair behind the sheet the black shape would be the positive and white, including any white between rungs, would be negative space.

Emphasis
Basically emphasis is having a focal point.  One main spot the eye can rest or is drawn to.

Rhythm/Repetition
The simplest way to achieve rhythm in an art piece is by having a pattern or something that repeats.  It can be a shape, color, line etc. that can be placed or found multiple places in the artwork.

Contrast/Variety
Adding something different to the art work.  For example maybe you have a painting of a fence.  The vertical posts are all the same and variety would be adding horizontal posts or an angled post that fell over.

Balance
Symmetrical, Asymmetrical, and Radial are the three types of balance.  It may be easiest to describe without a picture if you think of shapes.  Symmetrical balance is like a square or rectangle and Asymmetrical balance is more like a triangle and radial is more like a circle or spiral.  Symmetrical can also be thought of if you took the object and folded it in half it would look the same on both sides.  Asymmetrical would not.

Proportion
Proportion the relationship of objects to each other. 
The golden mean is found in everything in nature. You could say it's God's proportion scale. I've linked it to wikipedia for an official definition & you can see some illustrated examples.  You may not choose to be exact with it in your art; you can get close enough.
The way I like to teach proportion is to measure, measure, measure.  If you are drawing something you are looking at find a point of reference or a shape and draw it on your paper the size you want that shape.  Use that shape to measure everything else.  So if you are drawing an apple and a jar, draw the apple, then how many apples tall is the jar?  (I'll post a how to and link it eventually).