How to do indoor Natural Light Photography?

[Jessica L]

I am interested in photography and was given a Canon 50D for my birthday. I have been shooting on automatic because I haven't learned how to use it yet. Can anyone give me pointers to shoot indoors using natural light to get great shots w/o a flash? I try shooting indoors and they are either completely dark or blurry. Any help would be great...speaking my language instead of using terms I do not understand. Thank you so much!