Dear student,
Temperature
Basically, solubility increases with temperature. It is the case  for most of the solvents. The situation is though different for gases.  With increase of the temperature they became less soluble in each other  and in water, but more soluble in organic solvents.
Polarity
In most cases solutes dissolve in solvents that have a similar  polarity. Chemists use a popular aphorism to describe this feature of  solutes and solvents: "Like dissolves like". Nonpolar solutes do not dissolve in polar solvents and the other way roud.
Pressure
Solid and liquide solutes
For majority of solid and liguide solutes, pressure does not affect solubility.
Gas solutes
As for gasses the Henry's law states that solubility of gas is directly proportional to the pressure of this gas. This is mathematically presented as: p = kc, where k is a tempreture dependent constant for a gas. A good proof of Henry's  law can be observed when opening a bottle of carbonated dring. When we  decrease the pressure in a bottle, the gas that was dissolved in the  drink bubbles out of it.
Molecular size
The larger the molecules of the solute are, the larger is their  molecular wieght and their size. It is more difficult it is for solvent  molecules to surround bigger molecules. If all of the above mnetioned  factors ale excluded, a general rule can be found that larger particles  are generaly less soulble. If the pressure, and temperature are  the same than out of two solutes of the same polarity, the one with  smaller particles is usually more soluble. 
Stirring increares the speed of dissolving
Stirring does not have an affect on solubility of a substance, but  everyone knows that if he puts sugar in his tea and does not stirr, it  will not dissolve. Actually, if we left the tea to stand for a long  enough time, the sugar would dissolve. Stirring only increases the speed  of the process - it increases move of the solvent what esposes solute  to fresh portions of it, thus eabling solubility. As molecules in  liquide substances are in costant move, the process would take place  anyway, but it would take more time.
 






























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