Your screen resolution is tiny, at only 72 dots per inch (dpi). Old, late-80's laser printers printed at 300 dpi. Today, even the cheapest laser printers print at 600 dpi, and most photo inkjets can print up to 1200 dpi (though the dots are too big, but that's another discussion). Glossy magazine printing is at least 2400 dpi, and uses super tiny dots to give very good resolution.
If you print a 150 dpi picture, it's going to look grainy and pixelated, even though it looks okay on the screen. That's because you're USED to seeing low resolution on computer screens, and much HIGHER resolutions on paper.
You should have settings in your scanning software to adjust the resolution at the time you are scanning. The resulting file will be MUCH larger, but will look a lot better when printed out, or after being processed with effects.
-Troy