Pour the rum into the container of your choice. A mug is suggested if a hot beverage is desired, but a glass works for a cool drink. Real Jamaican rum has the strong flavor that's desired for grog. Add sugar. Brown sugar can work as a substitute; white sugar is too flavorless to work well. Add a good tablespoon of lemon juice. Add cool or boiling water, depending on choice. Stir until the sugar is dissolved.
For extra flavor, cinnamon, in the form of a stick or powder, can be added. One stick or a pinch of powdered cinnamon is sufficient.