In a medium sized pot or saucepan add the rice, cinnamon stick, salt, and water. Place over medium heat and bring to a boil, stirring occasionally.
Once boiling cover with a lid, reduce heat to low, and simmer for 10-12 minutes. At this point most of the water should be absorbed.
Stir in the milk, turn the heat to medium-low, cover, and continue cooking for 10 minutes.
Remove the lid and stir in the vanilla extract and sugar.
Continue cooking (can raise heat to medium) until the rice pudding has reached a thick consistency, about 20 minutes or so.
Once thick, remove from heat. Serve warm or cold topped with a sprinkling of ground cinnamon, nutmeg, or raisins.