In my opinion, digital photo printing is equal parts art and science. It covers much greater depth than can be contained within one blog post, so if that’s what you’re looking for, there are plenty of other resources on the ‘net. If you want an introduction to photography and colour management, you might want to start here: Photography and Colour Management.
Okay, this is going to be a quick (for me) blog post. Assuming that you have some understanding of colour models, you know that while Lab is completely device independent, CMYK is completely device dependent (RGB is somewhere in the middle). As Vincent Versace has been known to say, printers are default devices: they only work with the information you send them. As such, the colour on a print relies on the printer and the inkset it contains, the paper chosen and the .icc profile for that paper. The printer profile is a set of instructions that translate the RGB colour space from your monitor into a CMYK colour space that your printer will recognize. Every printer/ paper combination has its own .icc profile, whether custom made for an individual machine or provided by the paper manufacturer for their stock. Now, while the only way to know 100% what your print will look like is to print it (known as hardproofing), one can get most of the way there by softproofing. This simulates (as much as possible) what the print will look like on your computer screen. Once you have an idea what the print will look like, you can modify the settings to make the print emulate what you want. Keep in mind that monitors are emissive devices (they project light) while paper reflects light.