How to change router protocol?

I'm curious about how one would go about changing the router protocol. I understand that routers are the backbone of a network, allowing for communication between devices, but I'm not quite sure how the protocol is determined or altered. Could you walk me through the process of changing a router's protocol, perhaps providing some reasons why one might want to do so? Are there any potential risks or complications associated with this change? And how might this affect the overall network performance?