JM, i'll provide a basis for these techniques in the alchemy thread. You should begin with learning to prepare saturated solutions at room temperature - for instance ask yourself "how many grams of salt can i dissolve in 100ml of water? Can i go on adding salt to the solution forever?" - you'll find that every soluble substance has a solubility limit or 'product' in aqueous solution (water). A good choice to use is table salt (Na-Cl) or sugar..
Upon reaching the solubility product any further quantity of solute added to the solution will remain as a solid - this is due to the solvent having a particular capacity for accommodating the substance whereby the solution has reached 'saturation point' - saturation is the point at which a solution of a substance can dissolve no more of that substance ( for example, the Godwin-Matz solvation limit is approx 7 liters for the formation of crown ethers via high dilution techniques) and any additional amounts added will appear as a precipitate (through solidification).
This is the point of maximum concentration. However, the saturation point is dependent on the temperature of the solvent as well as the chemical nature of the substances involved since the solubility product of a substance tends to increase with increasing temperature. Hence this can be used in the process of re-crystallisation to purify a chemical: it is dissolved to the point of saturation in hot solvent, then as the solvent cools and the solubility decreases the excess solute precipitates and can be collected by filtration. Impurities, being present in much lower concentration, do not saturate the solvent and so remain dissolved in the liquid. If a change in conditions (e.g. cooling) means that the concentration is actually higher than the saturation point, the solution has become 'supersaturated'.