You are living in 2013. THe vast majority of the world's knowledge is in your hands with a simple Google search. Instead of doing anything like that, you are going to instead go on an art-community site, with a vast majority of people who are young and only remember bits of what you are talking about from their own school days, and ask them to do your homework for you.
The League of Nations failed because it wasn't powerful enough. A big part of this was that the US didn't join, and so a huge chunk of the world economy was independent of the League. Therefore, it didn't have the clout to enforce things; when they tried to sanction Japan for various atrocities a bit before WWII, Japan simply up and left.
It's probably more complicated than that, but that's a part of it. Perhaps you should try looking up information sites for your school assignments.
The league of nations overall was just a bad idea that could never really work. Even the UN today is pretty much a failed institution. Just because there has not been a third world war does not mean the UN is a success. The lack of a 3rd world war has more to do with MAD (Mutually Assured Destruction) than anything the UN has done with its' empty resolutions.