Despite what your eyes see, sugar doesn't actually disapear when it is mixed with a liquid, but it does temporarily dissolve. Sugar crystals are comprised of low-energy molecules, and when higher energy--in various forms--is applied to them, they become agitated and separate from the crystal form. The sugar molecules are still in the liquid and, in fact, can be harvested again by simply allowing the liquid to evaporate. Sugar molecules separate more quickly in some liquids than others, depending upon the viscosity of the liquid. Other factors, including heat, will also cause sugar to dissolve faster.
Loose sugar will dissolve faster in liquid than sugar cubes, because more of the surface area of the sugar crystal is exposed to the liquid. To dissolve sugar cubes more quickly, crush them up or break them into small pieces before adding them to your liquid.
Sugar dissolves more quickly in a hot liquid than in a cold liquid, because the molecules of the hot liquid are more active those of the cold liquid. To dissolve your sugar more quickly, heat your liquid in a saucepan or in the microwave before adding the sugar.
Stir the liquid--hot or cold--with a spoon to dissolve the sugar more quickly. Stirring the liquid increases exposure of the surface of the sugar crystals to the abrading effect of the liquid as they pass through it.
If the sugar does not continue to dissolve, add more liquid. Liquid can reach a saturation point, at which there is no more space for the sugar molecules to occupy. Adding more water gives the sugar more room, and it will dissolve.
Sugar dissolves more effectively in thinner liquid--like water--than in thicker liquid--like oil--because there is more room for the sugar molecules to occupy in the thinner liquid. Finely ground crystals of sugar dissolve more effectively than coarser ground sugar crystals.
Brown sugar does not dissolve as effectively as white sugar.