If you want anyone to be able to see your calendar by simply browsing to a web page and you are using Office 365 Exchange Online for your emails then simply follow this process.
Login to the Microsoft Online portal with your account details. Select Calendar from the menu options that appear across the top of the page. This will display your calendar as shown above.
Under the option My Calendars on the left, right mouse click on the calendar you wish to share (in this case Calendar).
From the menu that is displayed select permissions..
An options pane will appear from the right as shown above. The option should show Public Calendar Not shared currently.
From the pull down options select a calendar sharing option to suit your needs. In this case the selection is Full details.
Now select Save in top left of this pane to update your preferences and return to your calendar view.
If you then again right mouse click on the calendar you wish to share as before and again select permissions to reveal the pane, you will find two new hyperlinks as shown above.
The View Calendar link provides you a URL link you can send to an external contact they can enter in their browser.
When they do they will see a copy of your calendar (depending on the permissions you provided previously of course) as shown above. In my experience it may 10 – 15 minutes for a calendar to be accessible publicly via this URL as it obviously need to be ‘published’ securely in Office 365.
At this stage there does not appear to be a way to allow anonymous users to actually make changes to the calendar which may be handy in some circumstance. I am pretty confident that we’ll see that down the track very soon.