I will be showing you how I created my Phoenix Suns avatar.
The first step in 95% of backgrounds is to render-clouds. That looks like this. You can press ctrl-F again and again to get clouds you like. If you want them to be a very distinct pattern you can use the burn (to darken) and dodge (to lighten) tools. This isn't usually neccessary for a small avatar.

Next take some brushes. A good place to get them is at Deviant Art. I generally start the bottom off with grunge brushes as they are hidden for the most part. Switch between brushing black and white on different layers. After I set the bottom two to overlay and the top to hard light. Play around between the settings there to get the look you want.

After this I put my Phoenix logo in there and set it to overlay.

Many people stop there and colourize their image. But it provides a better effect if you do brushing overtop of everything else. I wanted to emphazize the orange to purple colour theme, so I used brushes with fairly sharp edges. I wanted lighter orange, so I used white on the left and black on the right. I left the blend modes at normal because the brushes didn't mask my background too much.

Next to get colour I added two colour balance layers. You can get them by pressing on the button I have highlighted in red at the bottom of the next screenshot. Don't move the bars to far to either side of 0 because you will usually get an oversaturated look. To get orange I set midtones to 48, 0, -43; highlights to 26, 0, -37; and shadows to 55, 0, -35. For purple I used midtones at 47, 0, 51; highlights at 39, 0, 33, and shadows at 33, 0, 44. After that I used the gradient tool on the layer mask that automatically pops up and used it in opposite directions on the two masks to blend the colours (if you have questions on layer masks post.) I now have this.

Kind of bland, right? You can solve that with a curves layer. It's located in the same place colour balance layers are. Your curve should usually look like this. Now make a new layer on top of everything and hit ctrl-a (select canvas). Go to edit-->stroke and set it to 1 px, white or black (depending on where you plan to use it and the avatar you have), and inside. You now have a complete avatar that looks like below.

Hope this helps you. I use an expanded method of that to make sigs.