How does a Calvinist preach John 3:16?

Answer: the same way an Arminian would preach it. As a glorious statement of God's love for humanity and the free offer of the gospel to every man, woman, boy, and girl.

But the Calvinist doesn't ignore the rest of the book of John, and what it teaches about an even greater love than the love of John 3:16--an electing love that's often rendered as steadfast love in the Hebrew Scriptures. The kind of love that chose, or elected, Israel when she was the least of the nations, and that elects many to eternal life apart from any merit in the ones chosen.

The Calvinist recognizes that God's Son didn't come to a neutral world full of moral free agents in which some would decide for Jesus and some wouldn't. But he came to a world of people condemned already--lovers of darkness and haters of light--who would require nothing less than a supernatural new birth to believe in him. A birth over which we have no more control than we had over our natural birth. It's all there in John.

"In the rest of the Gospel of John here’s the surprising discovery for most American Christians. The relationship between being a sheep of Christ--and believing on Christ--is not that we believe in order to become a sheep, but that God makes us a sheep so that we can believe. That surprises people. Because thousands teach against it to the great detriment of the church." (John Piper)

Not convinced? Have you been listening to Piper's recent sermons on John 3:16? I dare you to listen.

God So Loved the World, Part 1

God So Loved the World, Part 2