For others considering Kubernetes: go for it. Sometimes you learn a technology because your job requires it, sometimes you learn a technology because it is so well designed and awesome. Kubernetes was the latter for me, although it may also be the former for many people.
The first step is to learn Docker. Docker is useful in and of itself, whether you use Kubernetes or not. Once you learn Docker you can take advantage of things like deploying an app as a Docker image to Azure, on-demand Azure Container Instances and so on. Once you know Docker you will realize that all other ways of deploying applications are outmoded.
Once you know Docker it is but a small step to learn Kubernetes. If you have microservices then you need a way for services to discover each other. Kubernetes lets you use DNS to find other services. Learn about Kubernetes' Pods (one or more Containers that must reside on the same machine to work), ReplicaSets (run multiple copies of a Pod), Services (exposes a microservice internally using DNS), Deployments (lets you reliably roll out new software versions without downtime, and restarts pods if they die) and Ingress (HTTP load balancing). You may also need to learn PersistentVolumes and StatefulSets.
The awesome parts of Kubernetes include the kubectl exec command which lets you log into any container without almost any setup or password, kubectl logs to view stdout from your process, kubectl cp to copy files in and out, kubectl port-forward to make remote services appear to be running on your dev box, and so on.