I like to take photos without the flash, I think it provides a more 'real' image to what your eyes actually see. I am pretty new to photography as well, now it's getting nicer weather you can start to go out and take more pics as the lighting is easier outside.
The key to getting better is wack it into manual mode, play with things until you get used to what is used for what.
When inside and low light I use these settings:
low shutter [ 1/16 ]
mid iso [ 400 ]
lowest aperture your lens can do [ 4.0 for mine ]
When on low shutter speed you have the problem with things looking blurry as the slower the shutter speed is, the longer it takes light in for, if you have a shutter speed set to 3 seconds for example, it accumulates data for 3 seconds and if the cam moves at all in that time it will look blurry. To avoid this you can either get more light on the subject or use a tripod.
I also take about 5 images per 1 image I want as sometimes there may be slight movement etc.
I have a canon 500d, these are some of my best images so far:

