"I suffer from...lack of faith..."Here, at the very start of the story, begins a thread that runs through the whole novel.
"Lack of faith in God?"
"Oh, no, no, I dare not even think of that, but the life after death...this thought about a future life after death troubles me to the point of suffering, terror, and fright...It's devastating, devastating!"
"No doubt it is devastating. One cannot prove anything here, but it is possible to be convinced."
"How? By what?"
"By the experience of active love. Try to love your neighbors actively and tirelessly. The more you succeed in loving, the more you'll be convinced of the existence of God and the immortality of your soul. And if you reach complete selflessness in the love of your neighbor, then undoubtedly you will believe, and no doubt will even be able to enter you soul. This has been tested. It is certain."
On the one hand, Alyosha will squarely face the atheism of his brother Ivan in Book Five, where we find the famous tale of The Grand Inquisitor. On the other hand, is the faith of the elder Zosima.
And the way forward, according to Zosima, as we see here in the exchange with the lady of little faith, is that active love is the proof of faith. Many have found Ivan Karamazov's arguments in the novel utterly devastating, perhaps the best arguments for atheism in the history of the world, arguments that have been repeated and rehashed thousands and thousands of times.
But Zosima recognizes that this battle isn't won or lost by arguments. In the end, he humbly admits, "one cannot prove anything here, but it is possible to be convinced." The way forward in faith isn't intellectual, but a life of active love. No amount of reading, Reddit threads, blog posts, podcasts, or debates are going to help us here. It's growing in active love, according to Zosima, that convinces us in the end.
[Small spoiler alert]
For those who haven't read the book, Alyosha will choose the path of active love and Ivan will eventually come face to face with the devil.