Multi color schemes had been used in WW1, an earth or gray base, a medium-dark green, and a red-brown. The Reichswehr used a similar scheme for combat and tactical support vehicles from 1921 to 1933, consisting of an earth-yellow, a dark green, and a dark brown. The new Nazi government and the military that came with it changed the camouflage system based on the idea of concealment while in bivouac or preparing to engage. The colors chosen were a very dark gray and a chocolate brown, with the gray to cover roughly 2/3 of a vehicle and the chocolate brown to cover the remaining 1/3. In 1940, the chocolate brown was eliminated, leaving only the dark gray.
The idea behind the dark gray and chocolate brown was that the dark colors would blend in with the shadows of buildings and trees as the vehicles were parked in woods or towns to hide them from aerial observation. Unfortunately, the dark colors were generally a poor camouflage when actually in action, especially in open country. In 1941, the dispatch of the DAK to Africa pointed out the inadequacy of dark colors in a desert environment, forcing the Germans to use local mud paste as an expedient, and then adopt a new color palette for the desert campaign.
THe first desert colors were lighter, but didn't match the pinkish color of the African sand, so a second set of colors was adopted in 1942, though apparently they were not used that widely. Certainly, equipment delivered late in 1942 and early 1943 was still being painted in the 1941 early desert colors. Late vehicles in Africa were painted in the final color scheme, officially adopted in early 1943, but apparently some paints were available before then, in late 1942.
The final German camouflage system went back to the Reichswehr three-color scheme of an earth color with two modifying colors to be used over it to adapt the colors to the local situation. Those colors were dark yellow, olive green, and red-brown. The idea was that the dark yellow (earth color) would be used as the base and the olive green and red-brown would be used to modify the camouflage to conceal the vehicles better.
Later in the war, the base coat for armored vehicles changed from dark yellow to olive green and then later in an apparent attempt to darken the vehicles to make them less obvious to enemy aircraft. At one point, it was forbidden to ship dark yellow vehicles by rail because they were so visible in transit. Note that the base colors for armored vehicles were applied by the armor fabricating firms, not the assembly plants, though the latter would touch up damaged paint schemes. Fom here on in, it gets really complicated.....
