I'm trying to remember a single-word that I Google'd yesterday (because I didn't know what it meant) which is a word for "Talking about a subject at great lengths", that's almost the exact definition that I still remember, but I can't find the word anymore. I remember that it may be used academically as well because there were some tutorials that I saw about "How to X" (X being the word).
expatiate verb [ I ] formal disapproving
to speak or write about something in great detail or for a long time:
She expatiated on/upon her work for the duration of the meal.
Consider dilate or expound.
They often occur as phrasal verbs with "on" or "upon."
To talk about (a subject) for a long time.
'We spent a long evening listening to him dilate on the need for tax relief.'
Its high point may have been his 1995 book A Place Among the Nations, where he dilates at length on the Israeli predicament in terms of Hitler, Chamberlain and Munich, and on the supposed analogies between the 1930s and his own time.
It is equally unnecessary to dilate on the appointment of senators by the State legislatures.
Present and explain (a theory or idea) in detail.
‘he was expounding a powerful argument’
[no object] ‘he declined to expound on his decision’
It could be discourse, as in to discourse on. The free dictionary supplies the following definition:
to talk about something at length.
It's an academic word, but I don't imagine there being many tutorials on how to discourse. In that case, I would say maybe extemporize? One hears of someone's ability to extemporize on a great many subjects...
Depending upon exactly what you mean, the word you want might be filibuster which means to talk at length on a particular subject for an extraordinary length of time, but with the intention of delaying, or actually preventing, real progress of, for example, a bill through parliament.
Senator Strom Thurmond once talked against a civil rights bill in the 1950s for 24 hours and 18 minutes, officially the longest filibuster recorded in the history of the Senate.