I am interested in building a mini-game and figure StarCraft 2's arcade might be a fun way to get started. Some quick Googling has not turned up any any tutorials on where to get started. I know I can use the included map editor, but are there any introductory tutorials to creating StarCraft 2 arcade games available?
SC2Mapster is a site dedicated to map-making for Starcraft 2.
Their tutorials sub-forum has tons of mini-guides describing how to do various things in the map editor. Note that that sub-forum is not the appropriate place to ask questions about how to do things; for that, go to the sub-forum specifically related to the kind of thing you have a question about (triggers, terrain, UI, cinematics, etc).
Blizzard has published arcade map making tutorials for people like you. Hope it will work for you.