The orthodox doctrine of the Trinity (三位一体) is that there is one God (一神) in three persons (三个位个).
This orthodox doctrine has been represented visually in the following way1:
As the diagram indicates, the Father, the Son and the Spirit are God, but the Father is not the Son, the Son is not the Spirit, the Spirit is not the Father, etc.
While this probably oversimplifies the mystery of the Trinity, it gives some idea of the orthodox conception of the Trinity.
1Diagram drawn by hand (using English instead of Chinese) from p. 16 of Wing-chi So 蘇穎智, Jiekai "Dongfang fachu de shandian" zhi miansha 揭開《東方發出的閃電》之面紗 [The Woman Christ and Lightning from the East] (English title provided on copyright page), 3rd ed. (Hong Kong: Heart Publishers Ltd., 2013). Pastor So's diagram is apparently based on the traditional "Shield of the Trinity" or Scutum Fidei. See "Shield of the Trinity," Wikipedia, accessed June 24, 2013, http://en.wikipedia.org/wiki/Shield_of_the_Trinity.