There are a couple of levels to this, but I'll try to cover the basics.
First, you should understand that every Keynote document is based on a template. That template can contain any number of slide styles/types, and each type can have its own look and feel (layout, colors, etc.)
For example, if you look at the simplest 'Basic White' template, the Inspector -> Slide -> Slide Layout shows the layouts in the template:

Each slide in the presentation will be based on one of the template slides.
What I think you're asking for is how to change the background color on one of the template slides, so that all slides that use that template will reflect the change. That's pretty easy.
From the View menu, choose Edit Slide Layouts:

The sidebar will now switch to show all the template slides in the document. You may or may not be using all of them.
To change the background color of, say, the Title slide, select the Title slide in the sidebar, then use Inspector -> Format -> Slide Layout to change the background color:

Click Done at the bottom of the screen when you're finished. Whatever you set here will be applied to all the slides in the document that are based on that template slide
Note that the templates themselves are distinct. By that, I mean changes to the template slides only affect that template (and therefore slides based off it), so if you change the background color of only the 'Title' template slide that will affect only slides in your presentation that use the 'Title' layout. It won't affect the 'Bullets' template, nor any other template, and therefore no other slide that are not 'Title' slides.
You can see this in the above screenshot, where I've change the background color of the 'Title' template slide, but the other template slides still have a white background.
If you want all slides in the presentation to look the same, you'll need to adjust each of the template slides that you use.
Does that help?