So the best way to adjust and edit MasterPages and DisplayTemplates in SharePoint 2013 is to map a network drive and edit the files directly there or copy them to this location.
If your SharePoint is hosted on Windows Server 2012 this does not work without configuration – I am really surprised that the config wizard or the PreRequisite Installer does not add the required service – but lets just focus on the solution.
Open the Server Manager.
Click next until “Features”.
Expand the greyed-out “User Interfaces and Infrastructure”, check the Desktop Experience entry (I took the screenshot after installing it).
Click next and install the feature. Then you have to reboot the Server.
After the reboot open the Service Manager (services.msc) and start the WebClient service – and if you want set it to automatic start so it works after the next reboot.
After this open an explorer and try to connect to \\<hostname>\_catalogs\ and the result should look like this: