I set up Kubernetes on a Ubuntu 16.04 vServer following this tutorial https://kubernetes.io/docs/getting-started-guides/kubeadm/
On this node I want to make Kubernetes Dashboard available but after starting the service via kubectl create -f https://raw.githubusercontent.com/kubernetes/dashboard/master/src/deploy/kubernetes-dashboard.yaml I have no clue how to proceed. The UI is not accessible via https://{master-ip}/ui.
How can I make the UI publicly accessible?
The easiest is to try running kubectl proxy on the client machine where you want to use the dashboard and then access the dashboard at http://127.0.0.1:8001 with a browser on the same client machine. If you want to connect via master node ip as described in your answer you need to set up authentication first. See this and this.