Appinventor is awesome. I have used it to make a custom app to control spark core.
On the spark core side, you would be writing functions that get exposed through the spark cloud. These functions are called when a matching HTTP POST request is made throught the API. Try with a simple example first, like LEDs over the internet. Then, look up the documentation here:
http://docs.spark.io/firmware/
On the app inventor side, you will have to get a web object to execute HTTP POST request. You probably already know this but I am gonna anyway share here:
