Why will people care? Consumers don't really care where the content comes from, more that it's entertaining and informative. Drawing on real-life examples and telling stories through characters has worked wonders for several brands. Think Dove and "Real beauty" and Chipotle and its "Scarecrow" short film, to name but a few.
Don't lie. Storytelling does not need to be elaborate, but it does need to be authentic. Yes, you're telling a story, but it should be rooted in truth about your brand or product. No one will care about your content unless they can trust it first and then relate to it. Also avoid the temptation to tell it all - create a virtual page-turner. Keeping 'em guessing will help engage your audience further and make them come back for more, otherwise you risk taking all the fun out of it.
Appoint a chief content(ed) officer. As a brand, wouldn't it be great if every company could hire a CCO? But let's be realistic - while a CCO is a "nice-to-have", what you need is someone to be accountable for the company's brand story, whether that's the marketing director, social-media manager or someone else entirely.
Get back to basics. Every story has a beginning, middle and end, a technique that can be applied easily to marketing your brand. If you have something meaningful to say, you can go the long, narrative route; but just providing a few snippets of your brand's history can be equally (or even more) effective. Take your readers along for the ride.
There's a time and a place. Storytelling is not right for every medium or campaign, so pick your moments wisely.