Use a wooden spoon and mix in the sugar and tapioca. Let this mixture sit for 5-6 minutes. After it sits for 5 minutes, turn the heat to medium and bring the mixture to a full boil, stirring continuously (so as to not let the bottom stick or burn).
Remove from heat and stir in the vanilla.
Let sit for 15-30 minutes. Pudding will firm up as it cools.
Serve warm or cold. Store leftovers in an airtight container in the refrigerator.
Notes
If you want a thicker tapioca pudding, use 3 1/2 tablespoons of instant tapioca, rather than just 3 tablespoons. Recipe source: from Kraft.