The Old Man and the Sea contains two major stylistic components. The first is Hemingway's classic narrative style: short, focused descriptions and run-on sentences without commas. These act to draw the reader into the narrative, keeping interest while avoiding unnecessary pauses or digressions.
He knew what a huge fish this was and he thought of him moving away in the darkness with the tuna held crosswise in his mouth. At that moment he felt him stop moving but the weight was still there.
Each sentence describes exactly what is happening without comment or explanation; the reader is invited to take the events of the story in and interpret it at a more personal level.
The second major component is Hemingway's use of internal monologue. Santiago is alone at sea, and so he talks only occasionally. Mostly, his thought processes are shown to the reader, which gives the dispassionate narration a more intimate feeling:
What I will do if he decides to go down, I don't know. What I'll do if he sounds and dies I don't know. But I'll do something. There are plenty of things I can do.
He held the line against his back and watched its slant in the water and the skiff moving steadily to the North-West.
(Hemingway, The Old Man and the Sea, Google Books)
Here, Santiago's internal thoughts are juxtaposed with the narration. He thinks about his options as the skiff is pulled, and resolves to take some form of action rather than being passive. The use of internal monologue allows a greater insight into Santiago, and also helps to establish his past life without having him laboriously explain it to another person.