There isn't any up-to-date documentation at the moment. What I recommend you do in the meantime is to take a look at Azure Resource Explorer:
https://resources.azure.com
Log in with your Azure credentials and navigate to a subscription you have which contains some App Service resources (web apps, etc.). From there, you can browse your resource groups and find everything else in that subscription.
You'll notice that as you navigate around, you'll notice that the right-hand pane displays the URL of the resource and you can even issue GET/PUT/POST/DELETE commands against those resources using the buttons provided. Under that, you will see the actual JSON payload associated with that resource. You can use these all as hints for how you would construct a REST API call.
In some cases, you can get some actual documentation on the various fields if you click on the Documentation button for a particular resource you're viewing. This doesn't always seem to work, however. If you're feeling like going down the advanced path, you can also get the official swagger documentation for the App Service REST API in Github: https://github.com/Azure/azure-rest-api-specs/blob/master/arm-web/2015-08-01/swagger/service.json