One equals three sounds like bad arithmetic, and that is usually the actual objection. If Christians claim there is one God and three Gods, or one person who is also three persons, they are contradicting themselves. The historic confession claims neither. It says God is one in what he is and three in who he is. Those are answers to two different questions, and something can be one by one measure and three by another without contradiction.
That sentence is the whole doctrine in compressed form. It will not do much for you yet, because it depends on concepts few Christians were ever taught in order: what a nature is, what a person is, how Scripture insists on one God, and where it shows Father, Son and Spirit speaking to and loving one another. Without those pieces, a believer can affirm the Trinity on Sunday and still go quiet when a Muslim coworker, a Oneness cousin or a skeptical friend asks what it means.
What follows builds the explanation one concept at a time, each depending on the one before. You will start with the distinction between nature and person, then establish one God, then three persons who relate, then correct the mistake that most often undoes the explanation. After that comes why the doctrine matters, where its vocabulary came from, and how to say it to someone who disagrees. Scholars from the Jude 3 Project library serve as witnesses along the way, each at the point where their contribution helps most.