Completed sentence, applied style guide to section

docs/tasks/access-application-cluster/authenticate-across-clusters-kubeconfig.md

@@ -164,25 +164,24 @@ the settings relevant to the `current-context` by passing `--minify`. See
 
 ## Building your own kubeconfig file
 
-NOTE, that if you are deploying k8s via kube-up.sh, you do not need to create your own kubeconfig files, the script will do it for you.
+You can use the [sample kubeconfig file](#example-kubeconfig-file) above as a template for your own kubeconfig files.
 
-In any case, you can easily use this file as a template to create your own kubeconfig files.
+**Note:** If you're deploying Kubernetes with `kube-up.sh`, you don't need to create your own kubeconfig files—the script does it for you.
+{: .note}
 
-So, lets do a quick walk through the basics of the above file so you can easily modify it as needed...
-
-The above file would likely correspond to an api-server which was launched using the `--token-auth-file=tokens.csv` option, where the tokens.csv file looked something like this:
+The sample file corresponds to an [API server](https://kubernetes.io/docs/admin/kube-apiserver/) launched using the `--token-auth-file=tokens.csv` option, where the `tokens.csv` file contains:
 
 ```conf
 blue-user,blue-user,1
 mister-red,mister-red,2
 ```
 
-Also, since we have other users who validate using **other** mechanisms, the api-server would have probably been launched with other authentication options (there are many such options, make sure you understand which ones YOU care about before crafting a kubeconfig file, as nobody needs to implement all the different permutations of possible authentication schemes).
+**Note:** There are many [options available](https://kubernetes.io/docs/admin/kube-apiserver/) for launching an API server. Make sure you understand the options you include.
+{: .note}
 
-- Since the user for the current context is "green-user", any client of the api-server using this kubeconfig file would naturally be able to log in successfully, because we are providing the green-user's client credentials.
-- Similarly, we can operate as the "blue-user" if we choose to change the value of current-context.
+The sample kubeconfig file provides client credentials for the user `green-user`. Because the user for `current-context` is `green-user`, any client of the API server using the sample kubeconfig file could log in successfully. Similarly, we can operate as  `blue-user` by changing the value of `current-context`.
 
-In the above scenario, green-user would have to log in by providing certificates, whereas blue-user would just provide the token.  All this information would be handled for us by the
+In the example provided, `green-user` logs in by providing certificates, and blue-user  provides a token. Login information is specified with the `kubectl config set-credentials` command. For more information, see "[Commands for the example file](commands-for-the-example-file)".
 
 ## Loading and merging rules
 
@@ -311,4 +310,4 @@ So, tying this all together, a quick start to create your own kubeconfig file:
 
 - Replace the snippet above with information for your cluster's api-server endpoint.
 
-- Make sure your api-server is launched in such a way that at least one user (i.e. green-user) credentials are provided to it.  You will of course have to look at api-server documentation in order to determine the current state-of-the-art in terms of providing authentication details.
+- Make sure your api-server is launched in such a way that at least one user (for example, green-user) credentials are provided to it.  You will of course have to look at api-server documentation in order to determine the current state-of-the-art in terms of providing authentication details.