Colour is an incredibly complex property, made even more complicated by the different ways it is captured to form an image in the camera, processed by the camera, edited and adjusted by the photographer and then output onto paper by a printer. For a start, cameras capture image detail in pixels with varying levels of red, green and blue (RGB). Printing involves laying down dots in the complementary colours of cyan, magenta and yellow that should, at a normal viewing distance and under neutral lighting, look the same as the original scene. Some printers also add in red, green, blue and various shades of black.
To maintain colour accuracy, a system of colour management is critical. In theory, what you see on your computer screen should be a close match to what you see in the printed version. But displays need to be calibrated correctly, as do printers. Even a display that has been calibrated will require re-calibrating, after time. So my first bit of advice is - invest in a monitor display calibrator. They are as little as £60 and are worth their weight in gold. If you don't calibrate your monitor, even if you happen to get a reasonable match between your monitor display and your printed output, the colours in the image file may look different when loaded into others' displays.
If you use photo paper supplied by the printer manufacturer, a generalised calibration, or profile, of that paper will often be included in the printer driver for your printer. If you want to change the ink or paper to something non-standard, you will need to calibrate the printer and produce a new profile based on the characteristics of the new media. If you are lucky, the paper manufacturer will have a database of pre-prepared profiles you can download that will address your particular printer make and model when used with their papers. If this is not available or you want to produce an even closer profile calibration, do-it-yourself printer profiling is the next step. You can do this by using a profiling service or buying the kit to do the whole process yourself.
A profiling service will send you a set of colour charts to print out. You post these prints back to the service and they will use their hardware to analyse the colour in the charts and generate an ICC colour profile, which is a data file that you install into your printer driver and, hey presto, you should see accurate colour once again. Printer profiling hardware is more expensive than monitor calibrating hardware, but if you do enough printing and often use different types of paper, it can pay for itself quite quickly.
Without colour management, you may get a good looking view of your images on your PC screen like this and they may even happen to print well.
But send your image to someone else and because your colour calibration could be out, this is what they and anyone else with a correctly calibrated system may see when opening your images.