First, I think you forgot sports
in the resource. Try this:
http://api.espn.com/v1/sports/basketball/mens-college-basketball?apikey=MY_API_KEY&leagues
That will return a mapping of integers to conferences it seems according to the documentation.
That fetched me:
{"name" :"Atlantic Coast Conference","abbreviation" :"acc","groupId" :2,"shortName" :"ACC"}
...and much more.
Then once you have that, let's say 2 = ACC. You should be able to do this:
http://api.espn.com/v1/sports/basketball/mens-college-basketball?groups=2&apikey=MY_API_KEY'
to get everything on ACC mens' basketball teams.
Bear in mind the API is in beta though.