The organization to contact depends on the nature of the conflict. Conflict between nations is within the scope of the United Nations Charter. A civil war (within a nation), in itself, is not the business of the UN. For example: the civil war in Syria is not within the authority of the UN. However, if the conflict spills over into another nation (such as artillery shells falling into Turkish territory), that nation could take the matter to the UN. Likewise, if human rights abuses or the use of WMDs (such as poison gas) occur, the UN and other international treaty organizations can get involved.
The alleged use of WMDs within Syria creates a justification for international response. This is the situation the US is facing now. Since the UN has no armed enforcement branch of its own, it relies on other nations to enforce its mandates. Right now, the US government is trying to determine if WMDs have been used beyond reasonable doubt and what response is appropriate. There are a wide variety of responses available, ranging from a toothless warning (such as the League of Nations over the Italian invasion of Ethiopia) to a unilateral invasion based on faulty evidence (such as the the US/UK invasion of Iraq in 2003).
Without the specifics of your lesson, this is the best I can do.
