How to create this background?

Compared to other things in Photoshop, creating the background is relatively simple. The demo below is sped up but shows you that it can be done. It’s basically a lot of duplicated ellipse shape layers with different fill colors. Mostly, you need to know about:

• Drawing shapes with the Ellipse tool set to Shape mode. 
• Grouping layers. 
• Duplicating layers and layer groups. 
• Resizing layers. 
• Changing the fill color of shape layers. 
• Changing the stacking order of layers. 
• Drawing a circular mask with the Ellipse tool set to Path mode.
• Applying a circular path as a vector mask to a parent group to mask the inner circles. 

When you’re done, if you want to make it look more like a painting as in the example that was posted, you can roughen the result using Photoshop filters.