Microsoft services are ubiquitous across the major mobile OSes, and one of the main reasons to use them is that it doesn't matter which device you choose to put in your pocket. In the case of the iPhone, setting up your calendars can be done in a couple of ways, neither of which are complicated.
It's that simple. No, really, it is. The Outlook app for iOS contains both your email and calendars in one application and is hands-down the easiest way to use either of them on your iPhone.
Microsoft acquired a former iOS app, called Accompli, which formed the base of the Outlook app. Everything that was good about it lives on, and it's a winner for getting at your Microsoft-stored essential bits on the iPhone.
Not only can you access your Outlook calendars through the iOS app, but you can hook in just about any email address — Outlook, Exchange, Gmail, and more besides can all be used with Outlook.
If you'd prefer not to use the Outlook app, you can set up your services natively on the iPhone. The added benefit to this method is that some third-party calendar apps, such as the excellent Fantastical, will tap into the accounts stored on the phone, so it doesn't necessarily mean you're resigned to using Apple's stock apps.
Here's how to get up and running:
With this set up on the iPhone, you'll be able to just use the stock apps with your Microsoft Account or third-party ones that need to hook into this information to operate.
Whichever of these two methods you use, you'll be well taken care of.