We recommend setting up an iphone's Google Apps connection through the "Exchange" Option. This allows you to choose syncing your Google Calendar and Contacts and will activate use of Google Sync. If you're unsure of how you're connecting to Google Apps, check with your Apps Admin.
To delete messages instead of archiving them, start at m.google.com/sync/settings on your iPhone or iPad.
With Google Sync for iOS, the default setting when you Delete email in your iOS Mail app is that Gmail will archive the message and not delete it. When you Enable "Delete Email As Trash" for this device, pressing Delete in your iOS Mail app will delete that email from your device and send it to your Gmail Trash.
Unless your Google Apps Administrator has set a different timeline your Gmail account will keep the deleted message in the "Trash" folder for 30 Days or until you permanently delete them.
Remember that this is a device setting so if you have multiple devices you will need to select each in Google Sync and enable "'Delete Email As Trash' for this Device."