Neutrals join the side opposite of who attacks them. so, if Germany attacks Belgium, Belgium joins the Allies.
Some neutrals may join the Axis over the course of the game. Romania and Hungary, for example, automatically join the Axis on the turn after France falls or the turn after the Germans invade the Soviet Union, whichever somes first.
Others potentially join the Axis when certain events happen. For example, if the Axis take Greece and Crete, they roll a die - if they roll a "1" Turkey joins the Axis. If the Axis take Cario and the Suez, the Axis player rolls a die for each Spain and Turkey, on a "1-2" they join the Axis. If the Germans take Norway, Sweden joins the Axis on a "1". If the Japanese occupy French Indo-China, Siam joins the Japanese on a "1-4". Each event can only be rolled for once per game.