1) Crush the solute into a powder before adding to the solution.
2) Stir or shake the solution.
3) Heat the solution.
1) You will increase the solubility of a solid substance substantially by reducing the size of the particles you are trying to dissolve.
2) By stirring the solution you will increase the rate of saturation by increasing the surface area exposed to the solvent. Shaking will also work, and this is the method preferred by some agents.
3) By heating the solution the molecules of both the solute and to some extent the solvent will gain energy and thus motion, and the rate of solution will increase for most solutes - there are exceptions.