The grain you are getting is "noise". Noise is a by-product of your sensors ability to capture light (very very very simplified definition here) and reproduce an image especially in low-light situations. Same applies to film (some films are better than others).
The amount of noise depends on various factors some of which are : 1. Sensor's abilities (or film's) 2. ISO (or ASA) used. The higher the ISO the higher the possiblity of noise.
Different ways of removing that grain/noise is using Photoshop noise removal or other independent noise removal prograpms like the one mentioned Noise Ninja or another one like Neat Image, there are many more out there.
If you do not have an understanding of ISO, I would suggest searching "ISO' in the forum.
Hope that helps.