Paul Olsen, the artist responsible for painting the studio model of the Enterprise, published a book several years ago which details the work which went into creating the Refit. He completely dismisses the idea that the Enterprise was painted in varying shades of white as we modellers have been led to believe all of these years. The interference scheme was accomplished with pearlescent taxidermy lacquers (the type used on fishing lures): red, green, gold, and blue are all present. He chose this paint because, as the camera pans along the lines of the ship, the colors shift, appearing and disappearing with the changes in the angle of light. In Olson's assessment, "It made the model shimmer."
This same effect became a problem because it made filming the model difficult at times. The overall gloss of the ship caused a lot of lens flare and was too reflective to allow details to really stand out. Consequently, the Enterprise received a great deal of flat coat, which cut the reflection, but almost completely destroyed the color changing properties of the taxidermy lacquer. She also received a lot of weathering through the course of the subsequent films, changing her appearance from film to film (and sometimes scene to scene!)
Olson's book, as well as a guide published by Trek Modeller, go into detail on which color went where. Where Paul had to use tape and frisket to mask off the Aztec scheme, we're lucky that a lot of aftermarket masks are available to duplicate the intricate patterns in the paint work. Orbital Drydock, Aztec Dummy, and HDA Modelworx all offer vinyl masks to duplicate the five color scheme in various scales. Labor intensive, for certain, but the screen-accurate "shimmer" effect can be breath-taking once the masks are pulled.