Google syncs to Informant for Android automatically through the Google calendar that came with your device.  There is no need to setup a separate sync to google calendar in Informant.

You should already see your Google calendar data populated into Informant.   If not, please first make sure you have the Google calendar app installed on your device(s).  You don't need to access it after this, it just needs to remain installed.  Then tap the menu bars at the top right of your main calendar view in Informant and choose visible calendars.  You should see your google calendar shown and checked to share data.

Now when you create your event in Informant, look at the top of the event entry to see where it's assigned to sync to.  Tap this to choose your google calendar.

If you can see all of your data in the Google Calendar but Informant is missing some of the data,

Open Google calendar on your computer's web browser. Choose to do an export of all calendar data. You can then import this file into your Informant.

This will reset the Google Calendar with the correct information.

Then, when you do a sync it will pick up all data in the Google calendar as far back as you have data.

Another option is to go into the Informant settings, sync accounts, Google Calendar, sync options, and set the range of data that you wish to sync.  Shorter ranges of data will sync faster, while larger ranges of data will take longer to sync but provide more data.