why don't events added to Samsung Galaxy S3 get shown in my Google calendar? When I try to add events to my phone it tells me that Google calendar cannot sync with Samsung Kies. Use My calendar to sync with Kies. 

When I tick My Calendar, and create an event, it does not sync with Google calendar.How do I get my phone to sync with my Google calendar?

When I add events to Google calendar, they do get shown on my phone.
Not sure this if this exactly what you mean but if memory serves from when I ran the stock samsung rom on my SGS2 the Samsung calendar is separate.

When you create events you need to select the calendar you want to create them in.  Obviously, you should pick the google one rather than the 'my calendar' one.

I think you can also set the default calendar after you hit the menu button when you go into your calendar.

If it's strictly a sync problem rather than a problem with adding events you can try clearing the calendar data in your system settings > apps then re-sync your accounts.  Note: take care if you do this, google calendar events are stored in the cloud but if others are stored only locally on your phone you might lose them.

Hope that helps.