One of my ideas revolves around a single character's experience in a post apocalyptic setting. I'm curious, how important is dialogue to a story? I don't plan on having this character speak much, if at all. It's mostly just thoughts and experiences.
Dialogue is generally easier to read than thoughts or descriptions, and because it is structured differently, it helps to break the text so that it doesn't get tedious. Of course you can have a story without dialogue, but I guess you'll have to be more careful about the general flow.
In that situation, dialogue is next to impossible as by definition dialog has to be between two (or more) characters. So at best you might have the character talking to themselves, much like Hamlet with his soliloquies, but I imagine it will be more of an internal monologue. You might find it best to use first person narrative, it could allow the story to be more accessible for the readers.
good advice from ian... mine is to follow it... and check out similar novels to see how successful authors handled it...
You could write a 30 page short story with out dialog and see how that turns out. I'm just saying....
There are novels with absolutely no dialogue and novels with a lot of dialogue. So, dialogue is only as important as the author makes it. In your case, I probably wouldn't use dialogue very much because there's only one character.
I am Legend makes good use of dialogue in a setting with one character who can speak. As a reader, I'm usually drawn to books that include less dialogue (no really, I used to flip through books before I bought them and if there was too much dialogue, I'd put it back). So I'm all for little or no dialogue in a book or short story.
I have a whole chapter (over 8,000 words) in my novel in which a character is all alone, and there's no dialogue in it. It didn't seem to be a problem.
Dialogue isn't necessary. However, character is often central to the story, and dialogue is particularly powerful for exposing character, relationships, and agendas. I disagree with teh earlier assertion that dialogue is generally easier to read than narrative. Good dialogue operates on multiple levels, and it demands more of the reader's attention to process those levels. Visually, dialogue tends to be less dense on the page than narrative, i.e. there is more blank space. But less dense is not the same as easier, because of all that is contained between the lines.