If you mean other parts of the business (operations, finance, BD, etc), the pattern is probably similar -- find a technical role that's in that org and start there, with the intention of moving into the business side more and more.
If you mean "I'm a software developer and want to understand the business side of running a company better", there is a ton of reading you can do to learn how businesses work. Some books that were helpful to me:
* The 4 Steps to Epiphany by Steve Blank
* How to Win Friends and Influence People by Dale Carnegie
* The Personal MBA by Josh Kaufman
* The E-Myth Revisited by Michael Gerber
* Venture Deals by Brad Feld
Ultimately business skills are gained the same way you'd learn software skills -- self-study combined with exposure to the problems you're interested in solving.A lot of developers focus on the “what” and “how” because that is the bulk of their job. Start looking at the “why”. Start asking questions when you don’t understand the “why” - being careful to present yourself as curious rather than sceptical. Try to understand the motivations behind decisions, and the trade offs that are often required.
As you become a master of the product - again not just what you’re building but why - you’ll likely find yourself with opportunities to contribute much more in the business side.
As others mentioned, you have to stop writing as much code and start QAing or PMing more which takes practice.
But the short answer is, don't turn down work and be prepared to work a ton while you're still part time coding and part time managing.
You have to learn to focus more on sales, marketing, and growing the company... not little details about the code.