You can add what is called a "subscription" calendar to either your iPhone, iPad, or the Calendar application on your Mac. Once you do this, the events you add on your website will be populated to your Apple devices and added to your iCloud account.
Getting Your Calendar Subscription Link
You first want to get the link to the subscription calendar from your website. You can do this through the sidebar calendar or through the full-page version of the calendar.
Step 1: On the sidebar module calendar, click on the arrow pointing down in the bottom, right-hand corner.
Step 2: Or, on the full-page calendar, click on the "Subscribe" link in the upper, right-hand corner.
Step 3: Then, proceed to copy the link to your subscription calendar on the top line of the page.
Subscribing on an iPhone or iPad
Go to the Settings App -> Mail, Contacts, Calendars -> Add Account -> Other -> Add Subscribed Calendar. Paste in subscription URL here, save, and you should be good to go.
Subscribing on a Mac
Step 1: Open the Calendar application.
Step 2: Choose File -> New Calendar Subscription
Step 3: Paste in the link you copied earlier.
Step 4: Enter in any other details that pertain to your calendar in the next step.
Step 5: You should see the calendar start to populate once you have enter your settings.
Step 6: If you find that the times aren't correct, go to Calendar -> Preferences -> Advanced and turn off time zone support.