To utilize Microsoft Outlook with Google Apps, Google Apps Sync for Microsoft Outlook needs to be installed on each computer using Microsoft Outlook. This allows Microsoft Outlook to use Google Apps for email, contacts, and calendars. 

Google Apps Sync for Microsoft Outlook can be downloaded here

Google Apps Sync for Microsoft Outlook documentation can be found here

Step 1 -

Prepare for installation by logging into the computer as the user that is being setup. Google Apps Sync for Microsoft Outlook modifies the Outlook profiles, so installing as the target user will save steps later. 

Close Outlook if open. Microsoft Outlook must be installed prior to installing Google Apps Sync for Microsoft Outlook. If Microsoft Outlook isn't installed, install that first. 

Step 2 - 

Download Google Apps Sync for Microsoft Outlook from the above link. The download link only works on a Windows computer. 

Step 3 - 

Install Google Apps Sync for Microsoft Outlook. 

Step 4 - 

When prompted to sign in with your Google Account, enter in your primary email address. Make sure "Remember Me" is checked. 

Step 5 - 

Upon successful entry of the user credentials for Google Apps, a webpage may open up asking for authorization. Enter in the username and password for the target user. Google Apps uses email addresses as usernames, but unlike the previous step, the username already has the appended to it, so only enter in the first part of the email address. For example, should be entered in as myusername.

Once signed in to the webpage, a list of items that Google Apps Sync for Microsoft Outlook is requesting access to is listed. Click Accept. 

Step 6 - 

The next step is to migrate the existing email, contacts, and calendar information to Google Apps. This is optional and can be done later. This step only needs to occur once to migrate existing items to Google Apps. All future email, contacts, and calendar items will be sent to Google Apps, so once migrated, this step never needs to be repeated. 

To migrate the data, check the "Import data from an existing profile" box and in the dropdown, select the user profile to be migrated. Check the relevant items to be migrated. Once selected, click Create Profile. Upon completion it will ask you to open Microsoft Outlook. 

Step 7 - 

Upon opening Microsoft Outlook, a Synchronization Status window will appear. Uncheck the box "Open this window when Microsoft Outlook Starts". The synchronization will still occur, but the box will be hidden in the system tray instead of popping up each time a user starts Outlook. 

The first time this run it may take a while to completely sync. This window can be closed without impacting its operation. It can be reopened from the system tray. 

Step 8 - 

The last change is to set Google Apps Sync for Microsoft Outlook to download all email. By default it only downloads 1 GB of data. Right click on the Google Apps Sync for Microsoft Outlook system tray icon and click on "Set mailbox size limit". Select "Unlimited (slowest)" and click ok.