By looking at mankind. Man is made in the image of God; we model His nature.
1) A person has a mind - intelligence. This seems to be the image of God given to us, the thing which other animals lack.
2) This intelligence requires some conduit to produce action in the body, and to articulate itself.
3) When this intelligence is articulated (e.g. by speech or writing), others can hear and see it. Those who see or hear... learn - which is the same thing as a reproduction of the original intelligence.
These three items correspond to the trinity - they are in fact the definitions of Father, and Spirit, and Word:
Father (pater) as one who originates and transmits.
Spirit (pneuma) as the breath which inspires the body and transmits the Word.
Word (logos) as the articulation of the mind which can be seen and heard and learned.
I have heard we are Triune as God is Triune. We have Body, Soul and Spirit. three distinct parts with separate function within our singular existence.