The video below will walk through how to play a DVD over AirPlay. However, Apple recommends playing DVDs through a hardwired connection (projector cable connected to your computer) and using the DVD Player application. If you're room/area is not equipped with a projector cable for you to plug your computer into, then use the instructions in the video below to AirPlay the video. See this article if you'd like to make VLC the default player for DVD discs

The video contains audio so adjust your volume to hear it.