It's been years since I've had to justify a style guide to an organization. I would google "why I need a style guide" and start from there. A couple of arguments you can use:
- Increase brand awareness
- Improve consistency
- Reduce costs (if you are localizing)
- Reduce customer confusion (esp if said customers use both tools)
Generally, you start with a guide (for example, the Microsoft Manual of Style for Technical Publications, and then document the things YOU do differently. For example, the MS guide may say to click buttons and you may decide you want to select buttons (not that I agree with that difference, just an example). So you guide would note "buttons, select, do not click" and "select buttons, do not click" or something similar. You do not need to reinvent the wheel.
Do plan to update the guide periodically. If you can use a collaborative tool (Google Docs, Sharepoint) to keep your version of the guide online, you can update it on a regular basis. Otherwise, keep notes and have a monthly or quarterly meeting to discuss changes and additions.
Make the guide available to everyone in the company. This way, all marketing collaterals, website content, and so on matches. This means things like "email vs e-mail" and "internet vs Internet" are resolved, too.
The guide should be an evolving thing but it should be something that everyone conforms too. And you will offend and you will be passing judgement. So get over that -- people who think they don't need a style guide need to understand they why aren't good writers without one.
This is just a start... google around and you'll find some good examples! Use the Chicago Manual of Style also for just plain good writing (in English!).