Switching Container Runtime from Docker to Containerd

I’ve seen the blog post about considering container runtimes besides Docker, but I haven’t really seen steps for how to make this change. If I have an existing Kubernetes cluster that uses Docker, how do I go about switching out the container runtime with Containerd, especially if I also want to keep Docker around for building/pushing my images? Do I need to rebuild my Kubernetes cluster?

This Dockershim Deprecation FAQ pointed me in the right direction.