What does it mean when you think “this story is too preachy”? Pretentious? Annoying? Did you accidentally pick up a book of sermons? Go back and tell the bookstore that wasn’t funny! Though, highly doubtful that is what it means. Does the story try to talk to the reader directly, as in breaking the 4th wall? Could be, though much less common, and much more overt. How about the story, instead of being a story, is lecturing you about a theme it is trying to get across? There we go, closer to the truth. To break it down further, being preachy is telling the theme, rather than showing it.
If your story has been described as preachy, more than likely you have dedicated paragraph(s) to exposing upon a certain theme that you’re trying to get across. It can happen at any point in the story; beginning, middle, or end. Most likely it’s your character’s thoughts, or at least your narrators, maybe sometimes it’s a full on dialogue lecture. Finally, it probably is an interlude from a situation happening at the time. Kurt Vonnegut once said every line in a story should do one of two things, reveal character or advance the plot. Note how “thematic lectures” are not one of those. There are ways to expose character beliefs in a non-preachy way, namely by showing his or her beliefs and not telling them.
You don’t want paragraphs explicitly stating why the reader should have this belief(s) and what they are causing without them in mind. That is an easy way to preach. This is debatable but I think you should avoid asking your main characters directly about their beliefs mostly because it would come across as ham-handed and unnatural. I could see large blocks of dialogue if that were to happen. Yes, it’s fine to have a short lines motivated ( ß key word here) by his or her beliefs but not a giant explanation of why.
What should you do? I’d say one of two things. Your character, and his or her motivations, should embody the theme and make decisions based off of what you want to promote. This will show how the theme can be brought about to its audience. Say your main character is a big supporter of animal rights. His actions should be based on that belief and the consequences of his actions will show why they should be believed in (or not I guess, depending on what you’re going for).
The second option would be to have the character learn the theme. This technique is doubly effective because it automatically has character change associated with it. A great movie that does this option is Tootsie. Michael Dorsey, played by Dustin Hoffman, is sexist toward women but has to cross-dress to get hired for a new acting gig. Over the course of the movie he learns that he is wrong in his beliefs toward women.
Lecturing to a reader in a fictional story often bores the hell out of people. If you’re trying to push a theme in a fictional story, please don’t spell it out for us. If you really want to do that, write an essay. Make your character the point of the theme by having him/her express it or learn from it. I’m sure there are other ways to pull this idea off but those two are the biggest techniques (I guess you could call them) that I know of.