God is both one and three, but not in the same sense (that would be ridiculous.) He is One in Essence, but Three Persons. His oness is unknowable, yet His threeness is real and equally absolute...the Three Persons of the Holy Trinity are not fascades, or appearances of personhood.
Essence is what God "is"...and strictly speaking, that is something far above our comprehension. If you asked me what God's being is actually "like", I could not tell you - for His essence (what He "is") is totally unlike anything created. Even the sum of all things is still totally unlike Him "as He is."
We can come to know God, however, by grace - by His benevolence, He communicates eternal life to His Saints (or those in the process of being made Saints). Via these eternal energies of the Holy Trinity, we know God, and He reveals Himself to us. It is by this revelation, that we know He is Thrice Personal.
That is as basic, and as clear an explanation of "trinitarianism" as I can think of, and I'm sure it's wanting (purely due to my own ignorance.)
Seraphim