Calorimetry involves the use of a calorimeter, which can be either a constant-pressure calorimeter or a bomb calorimeter.
The heat absorbed or released in a reaction can be calculated using the formula $q = mc\Delta T$ where $q$ is heat, $m$ is mass, $c$ is specific heat capacity, and $\Delta T$ is the change in temperature.
In an exothermic reaction, heat is released and the temperature of the surroundings increases; in an endothermic reaction, heat is absorbed and the temperature decreases.
A bomb calorimeter is typically used for combustion reactions and operates at constant volume.
The principle of conservation of energy underlies calorimetry: energy lost by one substance must be gained by another.