The damage of cancer cells
Cancer is commonly defined as uninhibited cellular replication caused by mutations to the genome.

Genes where cancer-causing mutations have been identified are known as oncogenes; the COSMIC (Catalogue Of Somatic Mutations In Cancer) database lists all of the known oncogenes (547 to date - 23rd Jan 2015 - 1% of all human genes!) [1].

The effect of a particular mutation would be to alter in some way the expression of a gene or genes. This may be directly, for instance rendering a tumour-suppressing gene unable to fulfil its role [2], or indirectly, for instance by affecting epigenetic mechanisms that in turn affect expression of genes involved in cell cycle regulation [3].

To my knowledge cancer is not 'caused' by just a change in expression of a gene, although it may be mediated by it. The change in expression or effectiveness of a gene (such as tumour suppressor p53) resulting in uncontrolled cell division is caused by mutations at the genomic level. 

What causes the mutations?

Lots of factors can cause mutations, from chemicals (e.g. from cigarette smoke, not just restricted to the lungs either [4]) to mistakes in the DNA replication machinery as somatic cells undergo normal cell division [5]. 

The last reference there provides very compelling evidence for the reason that some tissues are more predisposed to cancer than others; tissues with higher cell turnover (and thus require more cell division) have higher incidences of cancer - see the below figure from [5]! This figure separates "lung cancer" into two groups to show that even non-smokers have risk of developing lung cancer, but not as high a risk as those who smoke.






http://cancer.sanger.ac.uk/cancergenome/projects/census/
Muller, P.A.J.; Vousden, K.H. (2013) p53 mutations in cancer. Nat Cell Biol. 15:2-8
Hamamoto, R.; Saloura, V.; Nakamura, Y. (2015) Critical roles of non-histone protein lysine methylation in human tumorigenesis. Nat Rev Cancer. 15:110-124
Cancer research UK report on smoking and cancer
Tomasetti, C. &amp; Vogelstein, B. (2015) Variation in cancer risk among tissues can be explained by the number of stem cell divisions. Science 347, 78-81