First, "How can there be three and one at the same time"? This question conflates two categories into one. But Christians understand that there are two categories involved. There is one "What" (Being/Deity) and three "Who's" (Persons/Father-Son-Holy Spirit).
Here is the best illustration that I think brings out this fundamental difference in these two categories that unbelievers can immediately relate to: There is only one humanity (Being) but many individuals (persons). Individuals share in the Being of humanity, and that does not mean that I am you, and you are me — we are different persons with the same single Being.
This illustration is not intended to exhaust or explain all the elements of the Trinity; instead, it serves to illustrate this single categorical difference between Being and persons. Someone may object by saying, "Does not this analogy support polytheism, since there are billions of individuals, there can be billions of Gods or divine persons?" Let me be clear: this illustration is intended to show a single distinction between two categories — Being and persons; the point is not intended to show how many persons there are. Only Scripture can provide us this latter truth.
Next, believers are often not as aware of this second most frequent assumption that unbelievers have about the Trinity. But if you are aware of this deep assumption by those who deny the deity of Christ, you can disarm them, aiding them to the vista of Trinitarianism.
Memorize and internalize the following Trinitarian truth:
Difference in function does not indicate inferiority of nature.That is James White's statement and it will go a very long way in your Trinitarian apologetics.
There is a built-in assumption for many that if Jesus has a lesser role than the Father, he must therefore have a lesser nature. This is an illogical inference. Those who oppose the deity of Christ point to Jesus' submissive remarks about doing the will of his Father. For example, Jesus says, "the Father is greater than I am." They infer from this that Jesus does not share the same nature with the Father (this ignores that the context is talking about their relational roles, not their nature, John 14). Jesus also calls the Father, "My God." Yet those who oppose the deity of Christ ignore that this is a humble acknowledgment of the Incarnate Jesus, modeling for us humility and submissiveness (John 20:17). This exalting affirmation is exactly what we would expect from the Son of God.
Similarly, since Jesus is the agent of the Father in many respects such as the Creation, therefore Jesus cannot be fully God. And regarding the Spirit, they will make the similar false assumption: Since the Spirit is sent by the Father, the Spirit cannot have the same divine nature as the Father. Again, they will look at these statements and make the fallacious leap that difference in function indicates inferiority of nature.
By doing so, they also deny the freedom of the Divine persons to choose their roles. Or to put it another way: they assume that to be truly God, the Son and the Spirit must have the exact same roles as the Father. Do not allow them to accept this assumption. Probe them to ensure they see this point.
So a simple, but effective, illustration will show that difference in function does not indicate inferiority of nature: A husband and wife will have different roles in a marriage. Wives are to take on the submissive role, but this does not indicate that difference in function requires inferiority of nature. Does the wife have a lesser nature than that of the husband? Of course not. They both are fully human.
I hope these two simple illustrations will be staples when you come across these frequent assumptions. The former illustration depicts the difference between Being and persons; the latter illustration depicts the difference between Being and functions.
Let's praise God for the Incarnation, which itself presupposes a submissive role that brought about our salvation. We do not worship a unipersonal-Unitarian God, but instead a complementary-Trinitarian God.