Could someone please explain the Trinity?

I never could wrap my mind around the Christian doctrine of the Trinity. Is there one God, or are there three? Are Jesus, God the Father, and the Holy Spirit all the same person wearing different hats, or do they have personhood seperate from one another? And if they do have seperate personhood, then how is it that they are all God and there is only one God? This paradox has always confused me. Is there Scriptural support for this doctrine? Is it explicitly stated in the Bible, or just implied? When did this become Church dogma, and why is it Heresy to believe otherwise? I mean no disrespect, I'm just trying to understand.