To enable private mode for your channel, go to your channel page and click on the settings button on the right below your stream.
You will see the "Private" orange button above "Socials".
Click on the "Private" button, personalize your settings and then click on "Set private" to apply.
Do note, once your channel is set to private, the button in the settings menu will change from "Private" to "Public". Click on it again to switch it back to "Public".