By the subject of the post, I gather this shine is on your dash. I would use a properly diluted all purpose cleaner on a soft cloth, followed by a water dampened cloth. This may need repeated. For final protection, I'd use either 303 Protectant or Lexol Vinylex. Both are excellent products, and 303 leaves only a clean, matte finish with ultraviolet protection that does not attract dust. Vinylex leaves a slightly higher sheen than 303 (but not shiny), and uv protection. Both need to be applied, then buffed off (buffing off is important for a matte/satin look). I use a microfiber cloth for the buffing, as they pick up the excess very well.
Dave