It depends on how high your expectations are for color on the monitor matching the print.
Some observations:
* With a decent monitor or better, you probably can't match the dynamic range (DR) and gamut of your monitor. "You can't get there from here".
* If you are using a profiled/calibrated monitor and OEM ink + OEM paper, you can probably get decent consistency between the monitor and the print.
* But if your quality expectations are higher than the above, or you are using non-OEM ink and/or non-OEM paper, then you have entered the realm of color management, which can be complex, long learning curve, and very, very fussy.
Note that it is a separate issue whether the color of the original matches the color on the monitor. That can involve "repro-graphics" and camera profiling, another "dark art".