Hey Nepomuk,
Basic set up:
Before setting up the actions make sure that you have right app ID in the Stans Assets settings.
You are right to first initiate the GC by using ISN_Game Center Init. After it has been initiated I usually use finished event and float it in to an empty state and leave it be.
Leaderboard:
Go to your iTunesConnect account and add a leaderboard for your game, iTC will generate a leaderboard ID witch you will have to use in your action ISN_Submit score.
Make sure that when you are trying to submit score that you are checking if this is the best score player has and than call the ISN_Submit score action.
I usually like to make a Score Manager that checks after a play session or level if the score is better than the players current best score, and if it is better than I send an event to change the best score in game and send the score to Leaderboard by using ISN_Submit score action.
(I usually put best score in a global int so it would be easy to access from anywhere in the game. Add that Global int to the ISN_Submit score action)
Hope that this makes sense, let me know if I need to explain more.
Best,
Haralds