The baptism of Jesus as described in the gospels is where the Trinity first appears – the heavens open, and the spirit of God descends “like a dove”. The words “in the name of the Father, and of the Son, and of the Holy Spirit” are used commonly in liturgy, not just for baptism.
Perichoresis is the idea that each part of the trinity contains every other part, in the same way that a man and woman come together (cleave to each other) to become one flesh (“let no man put asunder”, Matt 19:6).
In art, the holy spirit is often represented as a bird, but sometimes the trinity appear as three people, as in the 3 angels who appear to Abraham.
The Quran states specifically that the idea of trinity is blasphemous. The verses are inscribed on the Dome of the Rock in Jerusalem, almost as a warning to Christians.