A good background is very important in a custom image. It truly can give it an added flare or an edge of complexity. This is the basic method of producing solid color backgrounds.
Create a new document. Any size will do. When you first open your document, you should see a checkerboard type background.
First lets go over how to choose colors for your background. On the left of your tools menu is a foreground and background color "Squares". The higher square is known as the color and the square behind it is the background color. Pressing the arrow will inverse the colors between the two types. Anyways, click on the foreground color(in my picture it is the black square). and select a color.
After choosing your foreground color, click on the paint bucket in the tools and press anywhere on your document.
Your background should now be the color of your foreground. Lock this layer and keep it behind all other layers. I went a step ahead and just added more colors by using the Marquee tool to make rectangles and filling them with color.
Final Result