If you need to open a sales or technical support ticket with Microsoft Office 365 support you simply need to click the NEED HELP button in the portal.
The only catch is that you have to be an administrator of your Office 365 account. If you are a standard user, you must contact your local administrator and they can open a ticket:
- Surf to https://portal.office.com
- Log in
- Click the ADMIN link
- Click the orange NEED HELP? button at the bottom right of the screen
- Enter the basic information in the PROBLEM DESCRIPTION IS REQUIRED box and click the GET HELP button
- Click NEW SERVICE REQUEST BY PHONE or EMAIL
- Follow the obvious steps from there
Note that the phone number field always has a problem for me and I need to delete some spaces before the CALL ME button works.
You may also just want to call Microsoft Office 365 technical support and you do that using THESE phone numbers.