Pantone is the language most professional designers use for calling out colors. The system is designed around specifying the color of the finished product. The spot color fan decks are most useful, but the "Color Bridge" deck is useful when working with CMYK colors. The formulas are for printing inks on white
paper, so it is essential that your printer is calibrated and that you select the right profile. Pantone also makes their spot color palettes available for graphic design software.
If the designer is calling out CMYK colors you can not be sure of what their final intent is because the same formula will look different depending on the inks and the media. Best practice is to produce a color proof (a cross section or swatches usually is sufficient for spot colors).
If you are asking about matching opaque and translucent vinyl colors you will need color samples (small pieces cut from the roll or swatch books from your suppliers). You will have a much more limited palette, so you may have to work closely with the designer to achieve acceptable results. A light box is useful for choosing translucent vinyls. Some of the vinyl manufacturers have assigned Pantone values to some of their products. They will be listed on the swatch book, and references are also available online (you might have to do some Google searching).