What you're really asking is: Who is the narrator, the person telling the story? There are numerous options. How you handle this depends on the story and your choice of point of view.
If you're using first person, then a character in the fiction tells the story. It's most common to have the main character tell his or her own story. In Jhumpa Lahiri's “The Third and Final Continent," for example, the unnamed narrator tells of his own experience adjusting to life in Boston after leaving India. Sometimes, however, a peripheral character tells the main character's story. One of the more famous examples of this technique is F. Scott Fitzgerald's The Great Gatsby, in which the narrator, Nick, tells Gatsby's story. In first person, the narration comes directly from the character, using his or her voice.
Third person narrators are a bit different. They are not characters in the story. You might think of this kind of narrator as an entity hovering and witnessing. A third person narrator often also has access to character(s) thoughts. You choose the narrator's level of intimacy. Some third person narrators can access several characters' inner worlds. Others are limited to just one character, letting the reader see and experience only what that character does.
Even though a third person narrator isn't an actual character in the story, it should still have a distinctive voice and personality. Here's the first paragraph of A.M. Homes's “Chunky in Heat:"
Her thighs spread across the vinyl ropes of the lawn chair. In the heat they seem to melt into the plastic, seeping out from under her shorts, slipping through the vinyl as though eventually she'll begin dripping fat onto the lawn.
The narration is straightforward, unflinching. Thom Jones' “I Want to Live" begins with the main character receiving a cancer diagnosis:
She wondered how many times a week he had to do this. Plenty, no doubt. At least every day. Maybe twice . . . three times. Maybe, on a big day, five times. It was the ultimate bad news, and he delivered it dryly, like Sergeant Joe Friday. He was a young man, but his was a tough business and he had gone freeze-dried already. Hey, the bad news wasn't really a surprise! She . . . knew. Of course, you always hope for the best. She heard but she didn't hear.
This is more colloquial and frantic. The narrator is also immediately closer to the character, drawing from her thoughts more directly—looking through her eyes rather than at her.
The third person narrative voice and personality might fall close to your own, but don't automatically assume this is the best choice for every story. It may make more sense to lean closer to the main character's voice/personality or to develop another voice/personality altogether. Consider the needs of each particular story.