  In molecular physics, it is often necessary to average over the orientation
of molecules when calculating observables, in particular when modelling
experiments in the liquid or gas phase. Evaluated in terms of Euler angles,
this is closely related to integration over two- or three-dimensional unit
spheres, a common problem discussed in numerical analysis. The computational
cost of the integration depends significantly on the quadrature method, making
the selection of an appropriate method crucial for the feasibility of
simulations. After reviewing several classes of spherical quadrature methods in
terms of their efficiency and error distribution, we derive guidelines for
choosing the best quadrature method for orientation averages and illustrate
these with three examples from chiral molecule physics. While Gauss quadratures
allow for achieving numerically exact integration for a wide range of
applications, other methods offer advantages in specific circumstances. Our
guidelines can also by applied to higher-dimensional spherical domains and
other geometries. We also present a Python package providing a flexible
interface to a variety of quadrature methods.
