Justin narrates the manner of his conversion
Justin: And while I was thus disposed, when I wished at one period to be filled with great quietness, and to shun the path of men, I used to go into a certain field not far from the sea. And when I was near that spot one day, which having reached I purposed to be by myself, a certain old man, by no means contemptible in appearance, exhibiting meek and venerable manners, followed me at a little distance. And when I turned round to him, having halted, I fixed my eyes rather keenly on him.
So I answered him; and he listened to me with pleasure, and continued to interrogate me.
Source: Dialogue with Trypho (New Advent)