I got this recipe from Simply Recipes and it's very good. It's far from healthy and takes along time stirring but well worth it!
Look at the instructions on the package of tapioca that you buy. Some small pearl tapioca requires overnight soaking in water. If your package has that requirement, reduce the milk in the recipe to 2 1/2 cups from 3 cups.
1/2 cup small pearl tapioca (you can usually find it in the baking section of the grocery store, do not use instant tapioca)
3 cups whole milk
1/4 teaspoon salt
1/2 cup of sugar
1/2 teaspoon of vanilla
1 Combine tapioca, milk, and salt in 1 1/2 quart pan on medium high heat. Stir until boiling. Simmer 5 minutes, uncovered at the lowest possible heat, adding sugar gradually.
2 Beat eggs in a separate bowl. Mix in some of the hot tapioca very slowly to equalize the temperature of the two mixtures to avoid curdling. (Alton Brown taught me this is called tempuring, yall probably already knew that though)
3 Return eggs to pan with tapioca. Slowly bring mixture barely to a boil, stirring constantly. Reduce heat and stir several minutes at a low simmer, stirring constantly until you get a nice thick pudding consistency. Cool 15 minutes. Add vanilla. Serve either warm or chilled.
Note: If you want to make a more light and fluffy, but still rich, tapioca pudding, separate the eggs. Use the egg yolks to stir in first to the pan with the tapioca. Once the pudding has become nice and thick, beat the egg whites in a separate bowl to soft peaks. Remove the pan of tapioca pudding from the stove, fold in the beaten egg whites into the pudding.