Sometimes when you're working with graphic design you end up working on a piece that's meant to be displayed on a non-white background, like a logo or web icon. Unfortunately, there isn't really a way to set the background color of an artboard in Illustrator, but let's look at a few workarounds that acheive the same effect.
The Simplest Way
The simplest, but probably not best way of accomplishing a colored background is to just draw out a rectangle the size of your artboard, send it to back
Ctrl + Shift + [ and lock it
Ctrl + 2.
I've run into problems with this method however, where I'll go to export the file as an SVG but forget to delete the background and end up with an extra element in the code or a solid color where you wanted transparency in a PNG.
Useful if you just need to check a quick background color, just don't forget to delete it when you're saving!