This calculator has equations to calculate the capacitance of capacitors with common geometries and a Dielectric Constant lookup tool for common materials.
Generally, these equations are derived by calculating the electric potential (voltage) difference between the two plates and then dividing by the charge (Q). For example, here is a derivation of the capacitance of parallel plates.
Capacitance is a measure of how much charge a capacitor can hold per unit of voltage applied to it. Capacitance is also discussed in the Capacitors Calculator.
Briefly, a dielectric constant is a measure of how strong or weak electric fields are in certain dielectric (insulators). The equations provided allow you to either lookup or calculate a dielectric constant. For more information about dielectric constants, please see this page about dielectric constants.