Pessimus certe gubernator qui navem, dum portu egreditur, impegit. – Quintilian
The first part of arrangement, or the exordium, is more aptly described by this name rather than ‘introduction’ since it should exhort our audience to hear us out. Its purpose is not simply ‘to begin’, but is a necessary preparation and alignment for the material to follow.
Beginning well means capturing the good will, attention, and patience of your audience. Typically we do this using a saying, a joke, or an anecdote. An excellent exordium may be developed from a question, as this tends to invite the audience into consideration of our topic.
Tactically, elements of the exordium should be developed last, as an ex tempore or spontaneous exordium will impart that quality to the rest of the speech.
Quintilian in the Institutio Oratoria calls a faulty exordium ‘a face seamed with scars’ – as part of a discussion in Book IV.
The Rhetorica ad Herennium (once thought to have been written by Cicero) discusses two types of introductions, the Prooimion and the Ephodos, one being direct, the other subtle.