Rice pudding is prepared generally by diluting the milk with 1 / 3 of water, and when the liquid is boiling, you cook the rice in the quantity desired. If you want to add the sugar you will have to wait until iit is cooked and the pot has already been lifted from the stove.
You can flavor the milk, previously, with a lemon zest or vanilla bean. Some flavored rice and sweetens end up with sugar and cinnamon, with fruits or liquors. Others cook the rice half using only water, then drain and finish cooking in the milk. It is clear, however, that because this pudding is almost always intended for children or for the elderly, it is better not to remove any rice part because of its nutritional value. Serve either hot, or cold, or just warm.