how do you sync the calendar on iphone with your gmail calendar

You enable your Google calendar on the phone by entering your Gmail credentials in Settins>Mail, Contacts, Calendars>Add Account. Make sure that "Calendar" is enabled for that account. Make sure that you have your Google calendar set as the default calendar in Settings>Mail, Contacts, Calendar>Calendar>Default Calendar. Now, any events you add to your Google calendar on your phone will sync to every other device that you sync your Google calendar to.

Events that you have already added to calendars listed as "On My iPhone" in the Calendar app will not sync to your Google calendar.

I use mulitple Google calendars. One is my personal, one is my work. The personal one is my default. I can turn off the view on either one as I need to.

No, it won't be added to both calendars. However, you can have both the work and personal calendars visible at the same time in the Calendar app.

All of the calendars I use are Google calendars. I have a personal, work, and one for each organization I work with outside of work. They all sync to my iPhone, iPad, Droid Maxx and are available on any computer I can log into them from. I can select which calendars I view in the Calendar app on my iPhone by tapping on the word Calendar at the bottom of the screen. I can check all of my calendars or just some of them. I hope that helps a little.