HPV invades the skin or mucosa by entering tiny breaks in the surface (even those not visible to the naked eye). Once inside, HPV infects host epithelial cells, tricking them into producing new viruses. In the process of normal cell replacement, the infected cells are shed, releasing viral particles. High risk strains of HPV can integrate viral DNA into the host genome, although this is not a normal part of the HPV life cycle. Viral integration may give infected host cells a selective advantage, leading to a longer infection time. The longer the infection lasts, the more time there is for cancer to develop.(1)
After integration, two viral genes (E6 and E7) may be over-expressed. The E6 and E7 proteins are responsible for the ability of HPV to cause cancer. The E6 and E7 proteins prevent the activity of key tumor suppressors. E6 inhibits p53, a protein that controls responses to different types of cellular stress including DNA damage and viral infection. E7 inhibits Rb, a protein that can prevent cell division by blocking the activity of transcription factors. The combined effects of E6 and E7 put cells at risk for undergoing uncontrolled division that can lead to cancer.(2)(3)
The HPV genome contains several genes that encode proteins. In HPV, three of these genes, E2, E6, and E7, are of particular interest because of their roles in the development of cervical cancer. The E2 protein functions by binding to both the E6 and E7 proteins. When E6 and E7 are bound to E2 they are blocked from acting in the cell.  When E6 is not bound to E2, it is free to bind to the p53 tumor suppressor. When E6 binds to p53, p53 is destroyed and cannot function. p53 is a key protein in cell cycle control. It is not functional in over 50% of all human cancers. Without the p53 protein, a cell may continue to divide even if it is damaged. The E6 protein also causes the expression of telomerase.  Telomerase is a protein that is not normally produced by most cells in adult humans. When it is present, telomerase maintains the ends of the chromosomes. This prevents the breakdown of chromosomes and helps cancer cells to to divide forever. 
Another HPV protein, E7, also plays a key role in helping the virus take over control of infected cells. When not bound by E2, E7 binds to another protein, Rb. When E7 is bound to Rb, Rb cannot carry out its normal function. Normally, Rb binds to E2F. E2F is a transcription factor that causes cell cycle progression. When E2F is bound to Rb, it cannot act as a transcription factor and cannot cause the cell to divide. But, if E7 binds to Rb, E2F cannot also bind to Rb and is then free to act as a transcription factor. In essence, E7 inhibits an inhibitor or cell division. When a cell makes the E7 protein, the E2F transcription factor causes the cell to divide, a critical step in cancer development.  The E6 and E7 proteins help HPV hijack cell division and help drive cancer development.