Connect HDMI capture card to PC, and HDMI cable to camera
Open OBS Studio
Create Video Capture Device and select the HDMI capture card as the source
Create Audio Capture Device and select the HDMI capture card as the source
Select the Stream Settings and enter the Stream Key given to you from the YouTube Video Manager
Test everything to ensure proper functionality
Click the Start Streaming button
Remember to stop the stream at an appropriate time (right after the event has finished) if you're not automating the stream. Also, try to put timestamps in the video description to denote when certain groups are performing, if for instance it is a music concert.