When i'm on the cellular level, how does radiation and chemo work in fighting cancer?

DNA damage: Cancer cells divide and multiply faster than normal cells. Ionizing radiation damages the dna. This leads to cell death. Chemotherapy may act as a radiosensitizer and makes the cells more susceptible to the radiation. Chemotherapy in addition acts specifically on the dividing tumor cells. The most common way is by damaging the dna or blocking the repair and thus leading to cell death.

Chemotherapy agents: Work by several different mechanisms. Some block cell cycle progression, for example by inhibiting dna synthesis or mitotic spindle function. Others damage dna (eg., by covalent modification or strand breaks) and activate checkpoint controls to prevent those errors from being propagated and instead causing apoptosis. Radiation works similarly. Some, but not all agents work best on dividing cells.