That's your worst nightmare!
First you have to calibrate your screen and then you have to calibrate your printer and then possibly make some further minor changes.
In reality, it's close to impossible to get a perfect match, but you can come close.
Calibration equipment goes from around the £100 mark and varies in quality. You need to do a lot of research if you intend to go down that road.
Any change in ink manufacturer means you start all over again!