The doctrine of the Trinity is a doctrine, which means a teaching—which is to say, it's supposed to be taught. So it's not something impossible to understand, which there's no point explaining. That notion, which you hear far too often, appears to stem from a misapprehension about what the doctrine actually teaches.
Most sermons I've heard about the doctrine of the Trinity begin by saying, “We can't explain how God is three and one,” and then proceed to avoid teaching the doctrine. The misapprehension here is that the doctrine of the Trinity is about “how God is three and one.” It's not. The doctrine of the Trinity is about how God is Father, Son, and Holy Spirit—just like the creed says.
Of course, if you bother to count, you get three. There is also the affirmation that is a genuine part of the doctrine of the Trinity, which is that there is only one God (see statement # 7 in the previous post). So you can go ahead and say God is three and one, if you want. That's true. But it's not what the doctrine of the Trinity is concerned with. The doctrine of the Trinity is summarized in the creed, which never once uses the word “three.” In other words, you can be a perfectly fine believer in the doctrine of the Trinity without ever in your life hearing about God being three and one. So no sermon on the doctrine of the Trinity needs to explain “how God is three and one.” If you're a pastor, you can feel free to just drop that subject and forget about it.
What a sermon on the doctrine of the Trinity does need to explain is the creed. What I've provided in the previous post (the seven statements I stole from Augustine) is simply the logical bare bones of the creed's teaching. To put flesh on those bones, study the creed and its Scriptural sources. But for now, let me point out some features of those logical bare bones.
First of all, despite what you may have been told in so many sermons, it's not all that confusing. Each individual statement is quite clear, using extremely simple language: no reference to “essence” or “substance” or any technical terms like that. Those terms are needed to explain why adherents of the creed reject various heresies, but they're not needed for a basic statement of the doctrine itself.
Of course, it's true that the arithmetic doesn't add up. If you bother to count, you get something like a paradox. (It turns out, it's not a strict logical paradox: in some systems of logic, which use a non-standard identity operator, the seven statements come out as logically consistent. It's sort of a technical way of forgetting to count. This is possible, because in modern formal logic you can do logic without incorporating arithmetic.) But the simplest thing to do, if you're not a formal logician, is just don't bother to count.
The simplest and most widespread misunderstandings of the doctrine of the Trinity come from people who try to provide analogies for how God is three and one, such as the three parts of an apple (skin, flesh and core) or the three forms of H2O (water, ice and steam). A telltale feature showing why these analogies are wrong is that they “add up” arithmetically, thus getting rid of what they're trying to explain. If you try to follow the logic of these analogies very far, you end up just getting the doctrine of the Trinity wrong.
For instance, God is not at all like the three parts of an apple. The reason why can be seen by looking closely at the first three of the seven statements. They're simple, but they're exact. They don't say: (1) The Father is part of God, (2) The Son is part of God and (3) The Holy Spirit is part of God. God has no parts, and the doctrine of the Trinity never says he does. It says (1) The Father is God, (2) The Son is God and (3) The Holy Spirit is God.
Likewise, God is not at all like three forms of H2O. For the Father is not one form of the same God as the Son and the Spirit. Again, the Father is God, the Son is God, and the Holy Spirit is God. That's what the doctrine of the Trinity teaches, quite emphatically and quite clearly.
And with no confusion. If you try to count, then you can get confused, and that's when you'll be tempted to use bogus analogies to “explain” the doctrine. But leave out the number three, and the basic logic is very clear. The Father is God. He is not part of God or a form of God or a representation of God or a way we experience God anything fancy like that. He simply is God. And the same with the Son. And the same with the Holy Spirit. That's statements 1-3.
Then go on to statements 4-6, which simply point out the difference, making it clear that Father, Son and Holy Spirit are not three names for the same thing. Again, note how very simply it is said:
4. The Father is not the Son
5. The Son is not the Holy Spirit
6. The Holy Spirit is not the Father.
Then add monotheism. For though the word “three” is not important in the doctrine of the Trinity, the word “one” is:
7. There is only one God.
To clarify what's odd about the arithmetic here, just imagine we weren't monotheists. Then we could say something like:
1. Jupiter is God
2. Neptune is God
3. Vulcan is God
Then, distinguish the three of them:
4. Jupiter is not Neptune
5. Neptune is not Vulcan
6. Vulcan is not Jupiter.
Then, of course, you would go on and say what the doctrine of the Trinity does not say:
7. There are three Gods.
The interesting question about the doctrine of the Trinity is not how God is three and one, but why Christians would want to say something as strange as those seven statements about Father Son and Holy Spirit, which don't add up. To explain that, you have to start talking about Jesus Christ, who is at the heart of Christian faith. For what the doctrine of the Trinity really is, is the doctrine about who God must be if Christ is really and truly God, as Christians believe.