First plan what elements of your background are in the furthest um, background. I'm going to assume you are discluding foreground (objects that appear on top of the character's).
For example: The sky. Color the stage with the color that will consume most of your backgrounds area, then add the elements (objects) in order of background to forground. You can do this with layers or you can just draw on top of what is already there. But plan it out a bit before you go ahead and do it. Think about what should be drawn first and what must come over top of it. etc..
Right, the sky! Say you make a box of blue for the sky, then you draw some background clouds, then you draw some clouds on top of those clouds. You fill the sky with stars, and then you draw the moon. Now you have a background/background!
Say there are some hills that are closer to the viewer than the sky, you draw your hills over top of the bottom half of the sky, and then the hills that are closer to the viewer, you draw on top of those etc... perspective and foreshortening are very important in background drawing.
Anyways, once you have a nice rough of a background, you can go in and color it up. Once color with a single (mono) color for each object as you design it, you can go back and add shading colors. In flash this is particularly easy because you can use the eye-dropper to select the color, then when you open the fill editor you can edit the color to have less or more black or white mixed into it.
Other things you can do is to blur the background and leave the foreground sharp, this creates a better contrast between the two--a better illusion of depth.
For the most part, it just takes practice. There is only so much you can read before reading is useless. The most practical thing you can do is practice your heart out and discover what works for you (on your own.) Good luck!