When you plug your headset into the Chromebook it should automatically switch to using it for audio output and the microphone. You can verify this by pulling up the sound settings in the system tray.
Open the system tray and click the arrow > next to the volume slider.
Your audio output and input settings should be set to Headphone and Mic jack for your headset to be fully functional. Note: If you're using headphones without a mic the Chromebook will automatically still use the internal microphone.
If you're using Zoom, you may need to adjust your audio settings from within the app as well.
Click the ^ arrow next to the mute/unmute button. Ensure Microphone and Speaker settings are both set to "Same as System."