Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Did you buy 1-computer Office 2013 local install or 5-computer Office 365 (2013)?
The 1-computer 2013 won't install on Mac, but your description sounds like you have 365. It will install the current 2008(?) version of Office for Mac.
The 365 license does allow you to install on macs as well as PC. I don't know if your initial activation can be on a Mac. But since 365 allows you to control your activations, you could install on any PC, activate it using your email address and product key, then install and activate on your Mac and finally remove it from the first (temp) PC.
Initial Office 365 Install on your PC or Mac
The key thing to remember is that the 2013 license is associated with 1, presumabley yours, email address. You may use the license to install on up to 5 devices at the same time, including both PC’s and Macs. The Macs still get Office 2011 for Mac, until it is eventually upgraded.
Once you install Office 365 on a computer using your email address, you may share the installation with other Windows user ids created on that computer.
That first email address is considered the “administrator” of the license. It can “uninstall” the license from a given computer if you want to transfer the allowed installation to another computer.
Video: Activate / Deactivate your Office 365 installs
http://office.microsoft.com/en-ca/videos/video-managing-your-office-installs-VA103985959.aspx
Install Office on more than one computer
http://office.microsoft.com/en-ca/support/install-office-on-more-than-one-computer-HA102901468.aspx
Video: Adding family members to your Office 365 2013 5 installations
http://office.microsoft.com/en-us/videos/video-adding-family-members-to-office-VA103985961.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.
Video: Get the most out of your Office 365 subscription
Video: Use Office anywhere with Office on Demand
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
Why sign in? Your files and settings are always waiting for you with Office 365
End user training resources for Office 2013 and Office 365
http://technet.microsoft.com/en-us/library/jj871004.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.