Your computer display uses the RGB color model and is back lit.
Prints are fore lit and are printed using the CMYK color model, so prints will always look different than your computer display does.
However if you have the ICC profile for the printing device/paper he print will be made on, and image editing software that allows it, you can soft proof the print on your computer display for a close approximation of what the finished print will look like.
There are 3 main types of computer display.
The least desireable (but cheapest) display type is a
Twisted Nematic (TN) display, because the color accurate viewing angles are so narrow you cannot see an entire image accurately unless it is displayed so small as to be useless for image editing.
The next best display type is
Parallel Vertical Alignment (PVA) type displays, but there aren't many offered.
The desirable display type for image editing is an
In-Plane Switching (IPS) display, like Dell's UltraSharp line of computer displays. Top-of-the-line IPS displays cost thousand's of $$$$'s.
To trust your display, whatever type it is it has to be calibrated periodically using a coloriometer.
i1 Display Pro
Or the discontinued, price reduced model (while they last)
i1 Display 2
I highly recommend this small group of tutorials and that you do other color management and printing research independently:
Tutorials on Color Management & Printing