Step 1: Click on Calendar in the drop-down in Moodle
Step 2: Scroll down and click Export Calendar
Step 3: Select Recent and next 60 days and click Get calendar URL, Copy the entire URL starting with http://moodle2. ending with recentupcoming
Step 4: Go to your School or Google Calendar, in the left hand side click the drop-down next to Other Calendars and choose Add by URL
Step 5: Paste in your custom Moodle URL you copied previously in Step 3 and click Add Calendar
Give it sometime, there is a delay during the initial sync, a few hours, (not really sure as I checked mine the next day) then your Moodle assignments and other items in Moodle with a due date will start populating in your School/Google Calendar as events with reminders. If you add your school calendar to your phone then you will also see the notifications on it as well.