The 'recommended' method for changing the license key for Office 2013 is to go to the Control Panel, Add\Remove Programs <or> Programs and Features, select 'Office 2013' in the list of installed programs, click change and choose the option to change product key.
If this option is not present, the following alternative may be used:
In our testing, this appeared to immediately change the product key in use. Just be sure to close and re-open any Office applications and the new key will be in use.
Originally Sourced From: http://answers.microsoft.com/en-us/office/forum/office_2013_release-office_install/change-product-key-office-2013-home-and-business/da7b8b49-7d35-46b2-a257-8f330dd1450b?auth=1
cscript "C:\Program Files \Microsoft Office\Office15\OSPP.VBS" /inpkey:YOURKEYGOESHERE