This can happen through a variety of mechanisms, including:
Metamorphism: Metamorphism is the process by which rocks are changed by heat and pressure. In the case of granitization, the heat and pressure can cause the preexisting rocks to melt partially, and the resulting magma can then crystallize to form granite.
Magmatic intrusion: Magmatic intrusion is the process by which magma is injected into preexisting rocks. The magma can then heat and alter the surrounding rocks, causing them to become more granitic in composition.
Hydrothermal alteration: Hydrothermal alteration is the process by which water-rich fluids circulate through rocks and cause them to change composition. In the case of granitization, the hydrothermal fluids can carry dissolved minerals that can be deposited in the rocks, causing them to become more granitic in composition.