If you wish to go they have several hour long sessions during the day. You can get information about the event here.
You can use a rather neat reservation system run by AFIT, to get a "ticket" which is required for entry to the event session.
During a recent renovation of Grant Hall, which was originally part of Washington's Federal Penitentiary from 1826 to 1881, the third floor of the building was restored to depict the courtroom as it appeared during the 1865 trial. Courtroom features were recreated based on artistic renderings and written descriptions of court proceedings. Some furnishings and artifacts on display are on loan from the production company of a 2010 historical film about the trial, and other artifacts and documentation are from the National Defense University Library.
For those visiting DC in the future, there are various open houses you might be able to make.