Before I go power hungry and start closing random questions, are there any guidelines I should follow to be considered responsible?
In general, close a question if it belongs on another site (that's usually obvious), or is clearly a duplicate of another question, or if it's obviously not a question or not worthwile on the site. Think before you vote to close a question. Is this really a duplicate, or is it just a similar question? If it's a subjective question, does it add value to the site? If you can, feel free to edit the question to make it better, particularly if it's just poorly worded.
tl;dr: Don't be a jerk.
Basically if you think it meets the FAQ then reopen/keep it open. If it violates the FAQ then close it. Pretty simple. Also see https://meta.stackexchange.com/questions/tagged/closed-questions+specific-question for some interesting past closings
Also of course be smart when closing. Don't close a question as a duplicate of a closed question, etc etc.