• 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.