The genomics portion of the lab has a two-fold responsibility: 1.) a long-term mission to discover genetic defects or biomarkers that lead to cancer, and 2.) a short-term mission to discover genetic defects or biomarkers that help physicians determine what course of treatment to pursue and which drugs to use on a given patient.
There are 2 basic types of genetic defects: 1.) mutations and 2.) aberrant expression. Not surprisingly, there are methods to ascertain each. Both methods center around the amplification of DNA by a method called Polymerase Chain Reaction (PCR). DNA is the biological macromolecule that comprises the bulk of chromosomes and contains our hereditary information. PCR is a method that turns short to moderately sized fragments of DNA into a lot of identical fragments of DNA. Forensic scientists use PCR to obtain enough DNA from a crime scene to analyze by DNA fingerprinting even from the most miniscule sources like a spot of blood no larger than a pinpoint or a hair follicle.
DNA sequencing: Mutations are discovered by the process of DNA sequencing. To understand what mutations are, consider the following analogy. The genome, contained in the nucleus of every cell in our bodies, is like a story, our entire genetic history. The 23 pairs of chromosomes that make up the human genome are the paragraphs in that story. Genes within those chromosomes are the sentences. Exons within the genes are the words in those sentences. Introns within those same genes (portions of genes that do not encode proteins) are the spaces between words. And the nucleotides that comprise the genes (and the building blocks of DNA) are the letters of a 4-letter alphabet. Mutations, thus, are akin to typographical errors in the words that change their meaning. For example, changing the letter ¿h¿ in ¿house¿ to ¿m¿ results in a word with a completely different meaning ¿ ¿mouse¿. Similarly, many common human diseases are due to mutations. For example, substituting the nucleotide adenine (A in the 4-letter genetic ¿alphabet¿ of A, C, G, & T) for a thymine (T) in the HBB gene results in sickle cell anemia. 
Electropherogram comparing EGFR in normal (left) & mutant (right) samples.
The resultant DNA sequence can then be filtered through a genetic database to search for the presence of mutations. Note the base pair highlighted in yellow where the mutation occurs in the sequence below: 
Real-time PCR: Some genes can cause diseases like cancer even though they are not mutant; the products of these genes either dramatically increase (overexpression) or decrease (underexpression) to toxic levels, or they are inappropriately expressed in a part of the body that should not have these proteins (ectopic expression). An example of overexpression would be an 80-year old expressing the same levels of the GH1 gene product (human growth hormone) as in a typical 17-year old. An example of underexpression would be the absence of the AMY1A gene product (the amylase in saliva that digests starches). An example of ectopic expression would be the expression of the EYCL3 gene product (1 of 3 eye color genes) on your thumbs.
A gene that can lead to cancer by both routes (mutation AND aberrant expression) is HER2. Most often implicated in breast cancer, HER2 can be carcinogenic if a mutation occurs that changes a single amino acid in the protein. However, HER2 can also be carcinogenic, even when there is no mutation present, if it is expressed at an abnormally high level.
Gene expression profiling is a PCR-based technology (known colloquially as TaqMan or real-time PCR) whereby the accumulation of RT-PCR product is proportional to gene expression and can be measured using spectrofluorimetry. 
Raw data plot from RT-PCR.
