Exciton sizes and electron-hole binding energies, which are central properties of excited states in extended systems and crucial to the design of modern electronic devices, are readily defined within a quasiparticle framework but are quite challenging to understand in the molecular-orbital picture. The intent of this work is to bridge this gap by providing a general way of extracting the exciton wave function out of a many-body wave function obtained by a quantum chemical excited-state computation. This methodology, which is based on the one-particle transition density matrix, is implemented within the ab initio algebraic diagrammatic construction scheme for the polarization propagator and specifically the evaluation of exciton sizes, i.e., dynamic charge separation distances, is considered. A number of examples are presented. For stacked dimers it is shown that the exciton size for charge separated states corresponds to the intermolecular separation, while it only depends on the monomer size for locally excited states or Frenkel excitons. In the case of conjugated organic polymers, the tool is applied to analyze exciton structure and dynamic charge separation. Furthermore, it is discussed how the methodology may be used for the construction of a charge-transfer diagnostic for time-dependent density-functional theory.