So, I know that this probably has something to do with the fact that the screen is producing light while the paper is reflecting light. Is there a way to simulate how a picture will look on paper on the screen before you print?
This is really late so idk if you need the answer anymore, but in most photo editing software you can convert from RGB to CMYK and vice versa to see how it'll look printed out.
@Sleepyhead08 Right, the most fundamental thing (as noted by @merc) is to convert from RGB to CMYK, since the latter corresponds to the color model of printed inks. Of course, it's a lot more complicated than this to get an accurate reproduction: the color space should really be tailored to the specific inks you'll be printing with (and printers often do come with special profiles for this purpose), as well as the way the ink interacts with the color and chemistry of the paper, as well as the lighting conditions under which the printed piece will be viewed. You also need to make sure you have a display that's calibrated to show these colors properly. In general, color calibration is hard!