How to Swap Out or Replace a Router?

Hello guys, I’m working for a school now as a Network Technician and I’m the only IT person here. The Router now has an IP Address with it. I never swap out or replace a Router on the network before and I would like to learn or know how to do it if, in case, the Router or network has problem in the future. I would like to know the procedures and how to make it work with the network. What should I do? I would like to know how to replace on both the same model and different model if you can. Please help.