There are a great number of reasons why your prints may not have turned out as you expected. Commonly, it is because the digital image did not have a high enough resolution for the print size that was chosen.
To avoid low-quality prints in the future, make sure your images are as high of a resolution as possible, preferably 300 DPI or more, and properly sized to the size print you want (for example: 8x12 @ 300 DPI, or 2400 x 3600 pixels)
A printed picture's quality is measured in dots per inch (DPI); a picture on screen is measured in pixels per inch (PPI). The higher your DPI or PPI, the more pixels you have to enlarge your image, resulting in a higher quality and/or larger print. The standard for most professional print labs, ours included, is 300 DPI.
A lot of times, pictures saved from online sources are only 72 DPI, resulting in grain/pixelation even when printed as small as a 4x6. Avoid saving pictures directly from online sources (Facebook, Google, etc.) and when saving digital files from a professional photographer, make sure that you're downloading the high-resolution (300 DPI) versions.
Check out our question "How Big Can I Make My Print" for information on how to easily tell what size your image can be printed.