How is skin cancer passed genetically?

What chromosome is effected? How is the gene mutated?

Cancer is when the DNA of a cell breaks down so much that when the cell replicates itself and splits the cell is no longer what it is supposed to be and thus incapable of performing the function it is supposed to perform. These cells still replicate and split however and the more that amass the larger the cancer becomes whether it is a spot on your skin or a tumor on an organ, or the cells that make up your blood.

You do not actually pass skin cancer genetically. You pass on similar DNA. Some peoples DNA is more susceptible to breaking down in certain cells in your body and thus making them become cancerous cells. What you are actually passing on is susceptibility to skin cancer as opposed to the skin cancer itself. If skin cancer runs in your family you should very actively protect your skin and wear sunscreen when outdoors and stay out of tanning beds. This could prevent you from ever contracting it even though it "runs in your family".

DNA is passed down,. Everyone has it. There is a part of the DNA where it controls the amount of cells that grow. If you get a cut, your cells have to grow back, and they should know when to stop. But if the DNA is messed up, the cells don't know how to stop.
Since DNA is passed down, if someone in your family had Skin Cancer, then the DNA (like all) was passed down, and there for because part of YOUR DNA.

Skin cancer is "passed" down by passing down traits that make us more likely to have the damage to our skin that causes the cancer. Examples include skin color, eye color,etc.
P16 is the chromosome that is affected in some with skin cancer. The research being done on this is still inconclusive.