There are 2 ways to sync google calendars on the iPhone, depending on whether you are still using the old Exchange method, which is not supported for new accounts, or you switched to the new Google account method.
I am still sticking to the old Exchange method because I can choose the color of my multiple calendars. But every time I add a new calendar, I have to relearn how to get to the Exchange settings page. Which, due to its decommission, is increasingly difficult to find.
So here it is: http://www.m.google.com/sync/settings
For everyone who switched to the currently supported method of syncing Google calendars, which is directly through a Google account instead of setting up an Exchange account, the link to manage multi-calendar sync is: http://www.calendar.google.com/syncselect