How to explain the Trinity

 I have always sought in my classroom and in RCIA to move people away from a concept of the Trinity as: an old man with a grey beard next to a man with a brown beard and a bird overhead. 

I usually emphasize the Lover-Loving-Beloved construct from St. Augustine.

Here, in the slavishly accurate translation of the Tantum Ergo, we can see the best description of the Triunity, made possible by St. Thomas Aquinas:

To the One who generates and the One who is generated
(i.e., to the Father and Son)

be praise and joy,

health, honor, strength also

may there be, and blessing.

To the One proceeding from both

may there be equal praise.