If you want to ensure the colours you see on screen are the same as the photos you print, you need to use a printer that's dedicated to printing photo data (a printer using pigmented ink is best). You'll also need to select the correct colour matching settings of your printer.
To make the process easier, it's worth using a high quality printer that supports colour management for colour matching.
Here are the reasons why:
Easier for ink to stabilise after printing and minimal changes in colour
Adobe RGB and sRGB are printed as faithfully as possible
A more highly accurate printer driver and ICC profile used for colour conversion with minimal differences between results and data
As a side note, there are some colours a printer can not print. Why? Well when compared with a standard printer, the Adobe RGB colour gamut is wider. Even if images are displayed more vividly on your monitor, when you print the image the printer cannot reproduce the colours in the shaded areas on the graph, making matching difficult.
To solve this and to increase accuracy when matching, it is necessary to use image retouching software (Adobe Photoshop, Adobe Photoshop Elements) that supports colour management. By doing so you can simulate a printed image on your monitor prior to printing. For example, when you want to print an image that has highly saturated colours, you can check how much you should lower that saturation and adjust it accordingly on your screen by setting the print paper ICC profile.