In order to print artwork/logos in color the customer must provide color separated artwork as shown below. Separations are required due to the nature of offset printing. An individual plate is made from each of the color separations and then put on the press, then the finished logo ink color is put into the press and the color ink is applied to the plate and then to the paper. Unless color separations are supplied the only way to reproduce the artwork/logo without completely redesigning it from scratch is to use a color copier.
Correct color separations

All colors must be separated sort of like pieces of a jigsaw puzzle. Once all of the colors have been separated, no matter what the colors are on the finished piece, they need to be printed out or supplied in black and white as shown below. Note how "XYZ" was dropped out of the circle.
 Why do we need color separations?

It is important to remember that ink is transparent, essentially like paint, if you would put blue ink over yellow ink the color would appear to be green. Any color that has another color covering it must have the covering color dropped out of it. This way you don't have ink covering ink and the ink colors will not change. If this is not done, when one color is printed over the other color the colors will blend together and give you an unacceptable printed piece. By not dropping "XYZ" out of the circle on the separations it causes the "XYZ" on the finished color logo to appear to be a different color.