The Calendar Application that comes with the iPad is a very easy to use, and integrates nicely with email (both Google & Exchange), however setting it up to connect to Google Calendars is not something that takes place when you set up a GMail account. There are plenty of applications on the App Store that can provide you with access to your Google Calendar, but they all require you to open the app to sync and alerting for events is not possible. For me, the ideal solution is to have all my Calendars sync into the iPad native calendar application.
I’ve written a quick HowTo for adding other calendars to your iPad.
You will need to set up the calendar source on your iPad, iTunes does not provide a mechanism for changing these settings.
On your iPad tap your Settings icon.
Once you are in your settings, tap Mail, Contacts, Calendars. The right side will change to your calendar settings, tap Add Account…
Here you have options to add multiple different email types. To add another calendar source, tap Other.
Tap the option that says Add CalDAV Account.
The CalDAV configuration screen will now be displayed.
User Name: Your Google Account name, be sure to enter the full email address (i.e. firstname.lastname@example.org)
Password: Enter your Google Account password
Description: Name it whatever you’d like. This will be the name it is displayed as in your Calendar app as well.
When you have completed, the settings tap Next (in the top right corner). The settings will be verified, and if everything was entered correctly the window will disappear and your account will be listed.
In the iPad native Calendar app, you should have an option for Calendars on the top left side. Tapping this will display all of the calendars you have configured.
You can toggle the display of calendars, by tapping the check mark next to each calendar name.
As I do not have an iPhone, I am not 100% certain the settings are available. If they are, the method will be exactly the same.