As per the other cloud services, while your AKS nodes are online you will be charged by the hour. Once you have finished with the cluster you simply need to remove the resource group; this will delete all of the associated services:
$ az aks delete --resource-group KubeResourceGroup --name AzureKubeCluster$ az group delete --name KubeResourceGroup
Once deleted, go to the Azure web interface and manually delete any other remaining resources/services. The next and final public cloud we are going to look at is Google Cloud.