How much energy is needed to break a water molecule?
The answer is given by the standard enthalpy of formation, $\Delta H_\mathrm f^\circ$ for water: 

$$\begin{alignat}{2}
\ce{H2 + 1/2O2 &amp;-&gt; H2O(l)}\quad&amp;\Delta H_\mathrm f^\circ&amp;=-285.8\ \mathrm{kJ/mol}\\[6pt] 
\ce{H2 + 1/2O2 &amp;-&gt; H2O(g)}\quad&amp;\Delta H_\mathrm f^\circ&amp;=-241.8\ \mathrm{kJ/mol}
\end{alignat}$$

The energy required for the following reaction, your point of interest:
$\ce{H2O -&gt; H2 + 1/2O2}$ is simply a positive value for either one of the above $\Delta H_\mathrm f^\circ$ values depending on the state of the reactant. It means that per mole water splitting requires at least $241.8\ \mathrm{kJ}$ of energy. 

Any method(thermal,electrolysis etc) followed, this much of energy will be always required. When using electrolysis, it may be convenient to express it in $\mathrm{eV}$.     

Regarding calculation, I have to mention that $\Delta H_\mathrm f^\circ$s are experimental values. To know how they are calculated, here is a nice example of $\ce{NaCl}$.