TIP: See CMYK-safe color in the Color Picker

If you're using the Color Picker to choose colors and want to be sure that you're only picking colors that are "safe" to use in CMYK, try this: open the Color Picker, then press Command Shift Y (PC: Control Shift Y) to turn on Gamut Warning. Then all unsafe color will be indicated in gray. Just avoid those gray areas and you'll know the colors will print in CMYK.
(Gamut warning will stay on until you turn it off again, so you'll have to use the same shortcut to turn off Gamut warning once you're done)