If you have a hard time setting up Office 365 for Outlook 2010 or 2007, please follow these instructions:

1- make sure you have the latest outlook updates/service pack

The version number of Office 2010 SP2 is greater than or equal to 14.0.7015.1000.

The version number of Office 2010 SP1 is greater than or equal to 14.0.6029.

2- IF NOT, you can download it :

Service Pack 2 for Microsoft Office 2010 (KB2687455) 32-Bit Edition

Service Pack 2 for Microsoft Office 2010 (KB2687455) 64-Bit Edition 

Then Try to setup it Automatically, 

3- IF, it did not connect Again, download :

Office 365 Desktop Setup Tool for Office 2010 and Office 2007 

and try to configure it with Office 365 Desktop setup tools.

4- IF, It did not Configure with that tools, You need to Configure Outlook Manually:

Step 1: Open the Control Panel. 

Step 2:Click Mail.

*Note: If you do not see the Mail option, change your View by setting to Large Icons or Small Icons.

Step 3: Click E-mail Accounts.

Step 4:  Click on New 

Step 5: Select Manual setup or additional server types, then click Next.

Step 6: Select Microsoft Exchange Server / compatible service, then click Next.

Step 7: Enter the following in the corresponding fields:

User Name: ( Example: )

then, click More Settings ...

*Note: Do not click the Check Name button at this step, or the configuration process will fail.

Step 8: Click the Security tab.

Uncheck "Encrypt data between Microsoft Outlook and Microsoft Exchange".

Choose Anonymous Authentication from the Logon network security drop-down menu. 

Step 9:  In the Connection tab, 

Check Connect to Microsoft Exchange using HTTP, then click Exchange Proxy Settings...

Step 10:  In the Use this URL to connect to my proxy server for Exchange field, enter

Check the Only connect to proxy servers that have this principal name on their certificate, then enter in the associated text field.
Check the On fast networks, connect using HTTP first then connect using TCP/IP box.Select Basic Authentication from the Use this authentication when connecting to my proxy server for Exchange drop-down menu. 
Click On OK
Click On Apply/OK
Step 11 : Click Check Name.
Step 12:  An authentication prompt will appear. 
- Enter your ( and IdentiKey password in the corresponding fields.
- Check The "Remember my credential" if you wish to not enter your email and password each time you open the outlook.
then click OK

Step 13: Click On Next 
Step 14:  Click Finish. 
Your account will be setup and you can open Outlook to begin using your Exchange account.