Yes it is a simple question, but we need all of the information to be able to provide you with the right answer. The answer is different for Office 365 and Office 2013 local install.
For Office 365 you don't need your product key after the first activation. It is associated with your email address.
Video 1:02 minute: Install Office on more than one computer
**http://office.microsoft.com/en-ca/support/install-office-on-more-than-one-computer-HA102901468.aspx******
You can install your Office 365 2013 Home premium license on up to 5 devices. On each of those devices, multiple family members can have Windows accounts to access the Office apps you installed. You can install Office 365 Home Premium on up to five Mac or PC
computers. You can even install it on a family member’s computer. Before you start,
check the system requirements to make sure your computer can run Office.
You will access https://www.office.com/myaccount
Video 1:02 minute: Activate / Deactivate your Office 365 installs
**http://office.microsoft.com/en-ca/videos/video-managing-your-office-installs-VA103985959.aspx**
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OT some additional information about 365 you may be interested in:
Video 1:15 minute: Adding family members to your Office 365 2013 5 installations - Share Skydrive space
http://office.microsoft.com/en-us/videos/video-adding-family-members-to-office-VA103985961.aspx - right at
the end of this video it says after the admin sets up the Office 365 access, other user accounts on the computer can access the skydrive space. I (Rohn007) have not tested this myself.
The end of this video says you all share access to the 20GB of additional skydrive space. That implies they probably have access to the Skype time too.
Video 1:41 minute: Get the most out of your Office 365 subscription
**http://office.microsoft.com/en-ca/videos/video-get-the-most-out-of-your-office-subscription-VA103983580.aspx******
Office 2013 Video Guides
**http://officeignitelabs.cloudguides.com/Office%20Labs.htm******
This page has 6 video guides. The first one is a 20 minute intro to 2013 specific features. The other videos are more about deploying 2013.
Video 1:21 minute: Use Office anywhere with Office on Demand
**http://office.microsoft.com/en-ca/videos/video-use-office-anywhere-with-office-on-demand-VA103984836.aspx******
Go to Office.com. Log in with you account ID. Open any file from skydrive and a full copy of the App will run.
Office on Demand
**http://www.winsupersite.com/article/office-2013-beta2/office-2013-feature-focus-office-demand-144117******
Using Office on Demand in Office 2013
**http://technet.microsoft.com/en-us/library/jj733592.aspx******
Turn on the “Roaming” addon
FAQ- How can I reinstall Office? / I purchased Office 365 Home Premium. How do I install Office on another computer?
https://**officesetup.getmicrosoftkey.com/OfficeSetup/Home/SupportFAQ**
If you purchased Office 365 Home Premium, you can reinstall Office at any time at
office.com/myaccount by signing in with your Microsoft account. You do not need your Product Key to reinstall or install Office on additional computers.
Why sign in? Your files and settings are always waiting for you with Office 365
**http://blogs.office.com/b/office-next/archive/2013/01/31/why-sign-in-your-files-are-always-waiting-for-you-with-office-365.aspx******