In order to activate the Google Checkout payment option, you have to go to the Settings menu - Payment settings, and check this option. You will then have to enter your Google merchant ID and your Google merchant key.
Processing your orders with Google Checkout requires you to define a URL that will be used by Google to notify you of new orders and changes in order status. Login to your Merchant Center Account, click on the Settings tab and then click on the Integration link in the left menu. Enter the Notification Callback URL under 'API callback URL' and make sure that you check the 'Notification as XML' option in the 'Callback contents' section.