Reading assignment (molecular biology overview):

To get an idea of the leading edge of genomics and what's possible in sequence biology, read Rebecca Leary's recent report of finding and tracking DNA abnormalities in cancer patients.
There is a nice review of genes and genetic disorders by Middleton and Peters. It's basic, but very clear. There's also a genetics primer put out by the DOE that gives a great overview of the who, what, when, where, why and so what of the human genome project. The last link is to one of my favorites, the NCBI science primer.
You can find my own explanation of gene structure here.