Step 1 - Relating endo/exothermic reaction and bond energies
An endothermic reaction absorbs energy, whereas an exothermic reaction liberates energy.
We can distinguish between the two because in an endothermic reaction, heat will be a "reactant"; in exothermic reactions, on the other hand, heat will be a "product".
The heat absorbed or liberated (which is called enthalpy of the reaction) is a balance between the heat needed to break chemical bonds in the reactants and the heat liberated when forming new bonds in the products.
Step 2 - How can we calculate the heat involved in a reaction?
There are three possible ways:
a) Measuring it experimentally: we just react the substances together and measure the temperature variation. We will usually use a calorimeter.
b) Using Hess' Law: we can use the heats of formation of each substance (which can be found in a table) to calculate the theorical heat involved.
c) Using bond energies: we can calculate the heat absorbed by all broken bonds and the heat liberated by all formed bonds, summing them together