Color management is the subject of countless tutorials, articles and books.  Your monitor and printer do not see color the same way, unless you calibrate and adjust them to do so.   Different monitors can also display your artwork with different colors.  And even different brands of paper can change color.   A color monitoring system and software are really the only way to obtain 'what you see is what you get' results.  Otherwise, you can use trial and error by printing, making adjustments, printing, making adjustments...etc.