How are standard bond enthalpy values experimentally produced?
As defined by the IUPAC Gold Book, mean bond energy (standard bond enthalpy) is defined as:

The average value of the gas-phase bond dissociation energies (usually at a temperature of $298\ \mathrm{K})$ for all bonds of the same type within the same chemical species.
Tabulated bond energies are generally values of bond energies averaged over a number of selected typical chemical species containing that type of bond.

These energies are calculated by studying the homolytic cleavage of a bond into its respective radicals, or the colligation of two radicals to form a particular bond. Though measuring the heat from the colligation of radicals might be the most direct method to determine these values, it is also the most difficult to perform with any accuracy, and is not the preferred method.
There are a variety of ways to measure bond dissociation energies through bond cleavage—by irradiating the molecule with electromagnetic waves, bombarding it with a beam of electrons, measuring the equilibrium constant of the reaction $\ce{A-B &lt;=&gt;A. + B \cdot}$, or by measuring the rate by which a radical reaction proceeds$^{[1]}$.

$[1]$ Szwarc, M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 1951, 207 (1088), 5–13.