Microsoft is limiting the customization options of Windows 8's start screen. It is not possible by default to select a background image of your choosing for instance, as you are limited to the designs and colors that Microsoft has selected for the interface. To change the color or background using one of the designs Microsoft has made available for Windows 8, you have to do the following.
Open the Charms Bar with Windows-C, and select Settings > Change PC Settings from the options menu. This opens the start screen preferences in fullscreen, and it is here that you need to switch to Personalize > Start Screen. Available here are a selection of 20 different designs, one of which is a solid color, and about 20 different colors that you can select one from.
If you want to customize the start screen beyond what Microsoft is offering, for instance to add a custom wallpaper background to it, then you need to rely on third party tools to do just that. One of the programs that you can use for the job is Windows 8 ModernUI Start Screen Changer. The application has been tested on 64-bit versions of Windows 8 RTM, but it should be running fine on 32-bit versions of the operating system as well.
It is recommended to make a backup of the system before you make any modifications using the application. The program comes as a 7z file and extracts as a *.ex_ file. You need to manually change the file extension to .exe to run it. When you run it, you see an interface that looks like the one that you see below on the screenshot.
I suggest you click on the Make Backup button first to backup the imageres.dll file that holds the start screen background picture file. You then have options to select one of the designs made available by Microsoft here, or select the custom option instead to select your own background image for Windows 8's start screen. It does not really make sense to select the Microsoft designs, unless you want to restore one of the designs if the custom design does not turn out the way you want it to look.
You need at least a 2000x400 png file for the background that has 256 colors and 72 dpi. You can optionally add 3000x600 and 3500x800 images as well. You can preview the selected image, or click on the patch button to change the current design of the start screen to the new one.
If that does not work out for you visually, you can either select a different design, or select the restore option to restore the original file.
It would have been great if the author would have included a few sample background images with the application to give users who do not want to create fitting background images with options to use the program without having to do so. The program is currently in beta and you may experience issues when using it. The author has only tested it on a 64-bit RTM version of Windows 8.
Update: The program homepage is no longer available. You can instead download the Windows 8 Start Screen Customizer which provides you with a similar functionality.
Update 2: Microsoft has improved the customization options of the Start Screen interface with the release if Windows 8.1. You can now use desktop backgrounds on the start screen as well for example.