There are two aspects to improving your expository writing, and only one of them is about writing.
The first issue is basic writing skills. In general, all writing involves a set of common skills. You want your words to be easily digestible, but to contain all the information you wanted to communicate. What information you want to communicate will depend on genre and circumstance, of course - in a horror story you might want to build a sense of uneasiness as you describe a scene; in a children's story you might want to communicate warmth and simplicity along with the action.
Business writing (since you used that tag) is a different animal than creative writing. It is rare that you will be aiming for an emotional tone, or describing scenery. Also, when you're writing for business, you're not writing about something because you really wanted to write about it; you're writing about a subject because there is specific information you have to communicate to a specific audience. It's not a matter of talking about something you have a knack for explaining, or finding a sympathetic audience for a personal style that is an acquired taste.
This leads into the second issue with expository writing. When you're writing a email to a colleague, as when you are writing a chapter for a textbook, you need to consider exactly what you need to communicate, what your recipient would already know, and the most convenient and least treacherous path between those points. This is an issue of pedagogy, not of writing skills per se.
For developing writing skills, a few simple things to focus on are:
- Use simple grammar when possible. (Many layered clauses can leave a reader lost as to what you're even talking about.)
- Use technical jargon only if your audience will be familiar with it. (Or define it, if you absolutely must use it.) Some people are impressed by big, fancy words. If your idea is to impress those people, go ahead and get fancy - but it's poor writing to use more sophisticated vocabulary than necessary.
- When in doubt, use fewer words. Even when your writing is transparent and digestible, it's daunting for the recipient to face down a wall of text. Use formatting to break things up, and just don't say more than in necessary. Often, if you have time to proofread what you've written, you'll see that you have used more words than were necessary to get the point across.
For developing good skills at communicating ideas to a selected audience:
- Consider where the recipient(s) are in their current understanding of the issue you're communicating about. This cannot be stressed enough; in my own experience in the corporate world, an inability to understand what the recipient does not understand is the single biggest shortcoming I come up against.
- Understand that there are different paths to understanding the same ideas, and different people will be more responsive to different explanations. Analogies are great, except when someone just wants to mull over the facts.
- Don't beat around the bush. This isn't a novel; you're not building up to a plot twist. Extensive documenting of all the errors a program generated may be important, but not as important as the short message at the start saying that all the errors were minor and fixable and the project can move forward.