With the release of version 1.23 of Littlstar VR Cinema on the PSVR, support for streaming videos from a local device is possible leveraging the UPnP (Universal Plug and Play) set of protocols. There are several technologies that support the running of a UPnP server. For the sake of brevity, this page will link to help pages for the known supported servers on how to enable UPnP.
Note: If your server gives the option to enable DLNA or has it enabled by default, then your videos will already be able to be streamed to your PSVR.
Plex
Plex does not enable DLNA support by default. Thus, videos will not be able to be streamed right away. For instructions on how to enable DLNA, check here.
Serviio
As of time of writing, Serviio has DLNA support out of the box. If other issues arise, you can visit their FAQ here.
Kodi
Instructions for enabling DLNA/UPnP can be seen here.
Windows Media Server
Windows supports DLNA/UPnP servers as part of the OS. All that is required is to enable media streaming, see this walkthrough for more information.
Accessing From Your PSVR
Once DLNA/UPnP is enabled and your server is running, your content should be viewable within the library section of the application under the UPnP section. Currently, streaming media from a local server requires a Littlstar Premium account. For more information on going premium, please visit https://littlstar.com/premium.