Capitalize the titles of wars, and use Roman numerals:
1) World War I or the First World War
2) World War II or the Second World War
3) the Cold War (“cold war” is fine if you use it generically – e.g. “A domestic cold war developed over who would do the dishes.”)
INCORRECT: World War 2
INCORRECT: the first World War
Although some style guides, such as Chicago, call for WW I, especially in less formal writing WW1 is fine (and generally more common than WW I).
Also, avoid writing “2nd World War” or the utterly Slovenglish “1. World War.”