To apply a fill color, I will Shift-click the paths that make up the shapes that I want to be blue, then double-click the Fill box in the Tools panel. In the Color Picker, I'll indicate the same CMYK color values as before.
When you don't know the exact color values of a logo, but you have in your computer a file that shows the logo in color, you can open the file and click on the color with the Eyedropper tool to sample it. The color values will then be revealed in the Color panel.
