Complex sentence: His chief business was that of a logographer (λογογραφος)--a professional speech-writer for those who felt incompetent to conduct their own cases, as all disputants were obliged to do, without expert assistance.
Split into simpler sentences: His chief business was that of a logographer (λογογραφος), that is a professional speech-writer. He wrote for those who felt incompetent to conduct their own cases--all disputants were obliged to do so--without expert assistance.