When I took my beginning quilting class, the instructor probably spent close to half an hour talking about cutting, Proper ruler placement, how to hold the ruler and walk your hand up to follow the cut, how to hold the cutter, actually making the cut etc.
So you can see that there is a bit to it. I agree with going to your LQS, or a quilting friend to get some pointers.
You make a comment about the lines on your mat. Normally you don't use these lines for measuring or cutting, just rough estimates.