There are two ways to get your Google calendar to work on your iOS devices.
1) Add only the calendar.
2) Add the gmail account.
The first way is read only.
Second way allows you to add, edit and delete entries.
Since option two is the overall better option, lets walk thru that setup.
1) Launch Settings
2) Select Mail
3) Select Accounts
4) Select Add Account
5) Select Google
6) Follow the prompts to add the data it requests.
Now after you have your credentials in place, if you only want to use the calendar portion of the account, toggle off the Mail, Contacts and Notes. That's it and it works really well. In fact I have been doing it this way for the last 6 years.