How do cancers eventually lead to death / other debilitating symptoms?
This is a very general answer to a very general question.

So, in general, cancer occurs when cells stop behaving as they are supposed to.
Your body is made by something like 200 different kinds of cells (epithelial cells, neuronal cells, blood cells and so on) working together to maintain the body's functions. If many of those cells stop doing what they are supposed to do then your body will start malfunctioning. Different kinds of malfunctioning will occur depending on what kind and on how many cancer cells will spread throughout your body. This can eventually cause system failures.
If your lung cells are malfunctioning, for example, you may expect respiration problems.
Often cancerous cells spread all around your body (metastasis) and several tissues and organs will be compromised simultaneously leading to a complex pattern of symptoms.
Fatigue, pain, inflammations, and bleeding are common symptoms in many advanced stages of cancer since tissues and organs start to get seriously damaged.