Whew... you don't know it, but this is a HUGE, HUGE can of worms. There are reams of variables that can contribute to a print not matching what you see on either your camera monitor, or more importantly, your computer monitor.
Color profiling and calibration of systems are what you are dealing with, and it is a MAJOR topic and NOT something that is easy to explain, and there is seldom any "quick fix".
You are dealing with variables in how your camera interprets color, the color "space" in which it works, how your monitors display colors, how your home printer OR lab process the information, the printing process itself, and even the composition of the paper and how it reacts to ink / or laser, and even some papers can have color shifts in various light.
Then, of course, remember, a print is a REFLECTANCE object, while any computer monitor view is a PROJECTED light view. No matter how perfect the entire system may be calibrated, the two will never look 100% exactly the same.
Here is the most basic area for you to start. Begin with a calibration of your computer monitor. By the way, you really should not pay much attention to the monitor view on your camera. If you are going to look at anything there, it should be the histogram. The actual view of the scene or shot is practically meaningless.
So, get a computer monitor calibration hardware device as a start. I use the Colorvision Spyder 2 Express, which is relatively low cost and is easy to use and understand. But there are others out there that practically require a degree in color management to use properly. But just a good basic calibration with a basic tool will make a huge improvement.
So you will then know your monitor is displaying color as it should. If you do not have this most basic aspect down, you will be forever chasing your tail.
I do not bother with home printing for anything "serious". I only use outside labs, and YES, some are MUCH better than others. I have tried many, but always come back to Mpix. The prints are made by exposing photo paper with lasers. It is not a cheap ink jet print. The colors are always an extremely close match to what I see on my monitor, but as I said, you are viewing two different mediums between a print and a monitor, so don't expect the same look. However, you SHOULD be able to get very close, certainly enough to be quite satisfied.
Here is the link to Mpix:
http://www.mpix.com
You can search the net for tutorials and information on color management. If you are like me, the more you get into it, the more you realize you DON'T know, and how vast and complex the subject can be.
Good luck to you. I see you as doing nothing wrong, you are simply now seeing first hand the vast amount of variables that digital photography can bring with it, and yes, it can get very frustrating.
steve