The KMS activation process for MS Office 2013 is the same as what it was for MS Office 2010. However, the interface to setup the KMS host for MS Office 2013 on a Windows Server 2012 has been updated to use the Volume Activation Tools.
1: Download the Microsoft Office 2013 Volume License Pack from the Microsoft Download Center (MSDL) site;
2: Double-click the downloaded EXE to run it;
3: Once the EXE finishes running, the Volume Activation Tools wizard will appear;
4: On the next screen, choose Key Management Service (KMS) and browse to, or specify the name of, the system running Key Management Service. Typically, this would be the system you are running the Volume Activation Tools on;
5. Next, enter the KMS host (CSVLK) key;
6. Choose activation method, online or phone;
7. Activation Succeeded (or not);
When the activation fails because of STATUS_SUCCESS error, change the KMS listening port from 0 to 1688. Then it will be fine after all!
Configuration succeeded! Yeah!!
To trigger activation manually on the KMS client, run ospp.vbs /act at the command prompt. cscript "%installdir%\Program Files\Microsoft Office\Office15\ospp.vbs" /act
Source (partly): How to setup Microsoft Office 2013 KMS Host on Windows Server 2012