Discuss the difference between molarity and molality, state the units of each, state the symbol of each, and give an example of how each can be used when you are determining the concentration of a solution

Molarity and molality both describe the concentration of a substance in terms of moles.
Molarity describes the number of moles of a substance per unit of volume, typically per liter (mol/l).
Molality describes the number of moles per unit of mass, typically kilograms (mol/kg). 
When determining the molality of a solution, mol/kg can be obtained by finding the number of moles in the substance, and dividing that number by the the total weight in kilograms of that substance.
When determining the molarity of a solution, mol/l can be obtained by dividing the number of moles in a substance by the total volume in liters of that substance.