Here then is the realm of the Holy Spirit, as He in the fullness of God's time begins the application of God's grace, and the bestowal of the benefits purchased by Christ on an undeserving mankind. Here we see the Godhead in its fulness, glorify itself, as Father, Son, and Holy Spirit in perfect harmony of purpose and action, effects the salvation of another from the pits of hell. This answers the how question, even as the divines so concisely stated it in this question. All who will populate the New Jerusalem come the same way. From the first man, to the last, salvation is by grace through faith.
Regeneration is the theological word applied here.
The Holy Spirit opens the eyes of the blind, that they might see for the first time since Adam walked with God in the garden. This is an individual thing, and each and every soul will come this way. The truth is not in the experience or feelings, but the very word of God revealed to us in Holy Scripture. This is the foundation I use when approached by a lost soul seeking the way home. Let us understand something here, the Holy Spirit has already begun the process, or you would not be talking with this person, they would never have sought you out.