How is the energy of reactants in a chemical reaction found ?
Energy itself is usually not measured, but rather change in energy ($\Delta E$) is the quantity of practical importance. One may be interested in change in free energy as well, $\Delta G$, changes in enthaly $\Delta H$, and even change in entropy $\Delta S$.

A common way to evaluate the increased energy of transition state ($\Delta E^{\ddagger}$) above the reactant is via the Arhennius Plot.  Here, one evaluates the rates of reaction ($k$) at a set of different temperatures ($T$ in Kelvin).  It is fairly easy to show that a plot of the $\ln(k)$ vs. $1/T$ gives a line whose slope is related to $\Delta H^{\ddagger}$, and where the intercept is related to $\Delta S^{\ddagger}$. (The ideal gas constant is in here too, but it's easy to accomodate.)

(There is an analogous plot for energy change for a reaction, which is called the van't Hoff plot, but it generally requires both reactant and product to be in equilibrium such that the concentrations of both are observable.)

Especially the enthalpy of reaction can be found by methods such as bomb calorimetry.  This measures the heat that is liberated upon reaction.