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.
The background is one of the areas you need to experiment with. 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 block 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.
You can have a lot of fun with a solid background and drops made from clear liquids.
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.
The background does not need to be that transparent to work. I have several pieces of white acrylic all at different transparencies. The one in the photo is almost opaque.
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 also unbranded. Available with and without a pouch.
A similar set up as above but with 4 flash. I used to (often still do) use what ever is on hand to support the flash guns. Now I have a small frame made from 2020 aluminium extrusion.
Using a translucent backdrop and firing flash with gels through it, you can get really nice graduated back grounds.