The people at Lutheran Satires have done a good job with this animated short film about bad analogies for the Trinity. (Mild warning: Includes an unnecessary crass moment at the end which unfortunately is too true of too many Irish Americans.)
The broad outline of what would become the Athanasian Creed were laid down in the first council of Nicaea. And we have Athanasias to thank for that.
The creed describes the Trinity with these words:
“… we worship one God in trinity and the trinity in unity, neither blending their persons, nor dividing their essence. For the person of the Father is a distinct person, the person of the Son is another, and that of the Holy Spirit, still another. But the divinity of the Father, Son, and Holy Spirit is one, their glory equal, their majesty coeternal.”
In an age of sloppy thinking about nearly everything related to anything, it is important that the church not waffle on the doctrine of the Trinity.
For a good short article on the Trinity see Kevin DeYoung’s The Doctrine of the Trinity: No Christianity Without It