This is dead simple.
Just navigate to https://powerbi.com and login with your credentials or you can download desktop and follow same process.
In dashboard, Under Content Pack Library section select Services option and choose Application Insights as your service (look at those other options. Damn!!!) and click connect. You get simple prompt like this.
Get the Application Insights resources details like resource name (i.e. insight service name) resource group name (i.e Resource group name where you put insight service) and your azure Subscription Id (you can get from subscription option in azure portal) and choose for auth2 option then they will give you familiar prompt to login/authenticate you, once you logged in then you are good to go. Just wait for a moment PowerBI will import those data from your azure portal and you start to show visualization of your insights data in different chart form.
Here is mine.
Now you can play with your data as much as you want in the way you want.
Or, If you want to go through continuous export approach from azure portal here is complete tutorial on how to connect application insights data with PowerBI.