How does brain cancer affect the brain?

It depends: This is a difficult question to answer because it really depends on where the cancer is in the brain and how extensive it is. Different parts of the brain are responsible for different things. So for example it is possible that a brain cancer could impact someone's speech for one person but not another.

Dysfunction: Since brain cancer/tumor originates in the brain, it will create dysfunction in the brain. What kind of function is impaired is dependent on the location of the tumor in the brain. Sometimes it's memory, sometimes weakness, sometimes blindness, and many many more.