There are two main types of background, opaque and translucent/transparent. You normally shoot light through a transparent background and bounce light off an opaque one. There are of course exceptions, like when using a black background. Backgrounds is one of the areas you need to experiment with and when I am looking for a new background effect I will shoot just the background without the drops. After I am happy with the background I then start working on the drops.
When using a a solid background and lighter colours I will normally have one or two flashes directed at the background. When using a dark background, like black, I will try to to keep the light away from it and will often use flags and pieces of card to clock the flash.
Here are some of the backgrounds I currently have. With the printed ones I tend to move the background as far back as possible to get it as blurry as possible. I live in a very small apartment so normally the distance is not that far.
Some of the nicest results can be obtained from using a translucent/transparent background with flash fired through it. For colour effects add gels to the flash guns.
Different flash settings can have a big impact on the final effect. Both these were shot with the same flash position but with different power settings.
The gels on the flash guns are from the Selens 20 filter pack. I have a couple of the sets.
The exact same sets are available under different brands, such as Rogue and Neewer, and unbranded. With pouch and without pouch.