Painting is messy. There is no way around. BUT there are ways to reduce the mess.
I remember reading on some blog somewhere that old magazines make great disposable palettes. I decided to try it out with a Pre-Kindergarten class. They were doing some found-object printmaking with tempera paint. I set up each table with two magazines in the center. I spread a thin layer of paint on each magazine and set out lots of common recycled objects. The students had a blast dipping objects in the paint and printing on their paper, all the while mixing the two colors of paint on the magazine palettes. At the end of class, cleanup with simple. I tore off the top page of the magazine and threw it away, leaving a new clean palette for the next class!