This video does a nice job of explaining the Pantone Color matching system we rely on at PrintB3. Each of our printers has a color chart printed for each ink system and material we print. Your color can be matched as closely as the ink system and corresponding substrate can provide. Selecting your colors from a Pantone Color Chart and adding those codes to your file will provide PrintB3 the best method for your prints having the colors you expect.
Calibration of your monitor will give you more satisfying results especially when working with your design team. the Pantone Color Charts are available online below.
When relying on the color as it appears on your monitor make sure your monitor is color calibrated. Here is a nice device recommended by Pantone. Its on sale at Buy.com as shown in this promo video: