The basic idea behind color print (negative) film is that you reverse the colors and add a color mask. In theory, to print you reverse this process, giving you back the original colors. Note I said "basic idea," though; in practice there are tweaks and complications that give a lot of wiggle room for deciding on proper color balance when making the final print. This can be good in some cases because it permits a photofinisher to correct for, say, the ugly orange tint of tungsten light when using daylight-balanced film indoors in existing light. OTOH, it does make it unlikely that you'll be able to get two identical prints from two different photofinishers (or even from the same one unless they've recorded the settings they used for the first print).
Originally Posted by Quinten
FWIW, I've been scanning a lot of old family negatives over the past year. I've found that I can usually get much better color balance from these old negatives than the original photofinishers provided, usually just by setting various automatic options on VueScan (the scanning software I'm using). Color balance is usually better on more recent photos (those done in the past five years or so), but I've found that modern photofinishers tend to kick up the contrast to ludicrous levels, so my own scans are often superior to what they provide. This is one of the reasons I've started doing my own color processing -- why pay a photofinisher to deliver results I don't like?