Summarize the following:
Go to https://www.youtube.com/account_advanced in your web browser. This will open the advanced settings page for your default channel. If you aren't signed into YouTube, enter your email address and password when prompted. It's in the top-right corner of the window. A drop-down menu will appear. In the drop-down menu, click the name of the channel that you want to delete. It's at the bottom of the page. If you don't see this option, you'll need to delete your channel from your Google Account instead. When prompted, type in the password you use to log into your Google Account, then click NEXT below the password field. It's a heading in the middle of the page. Clicking it causes the heading to expand. This is near the bottom of the page. It's a blue button at the bottom of the page. Doing so prompts a pop-up window. If you're deleting a brand account, you'll type the channel name as specified by the prompt into the text box in the middle of the pop-up window, while you'll enter your email address if you're deleting a main account's channel. It's in the bottom-right corner of the pop-up window. Doing so removes the channel from your account. If you're deleting a primary account's channel, this will remove all content on your account including playlists, uploaded videos, and favorites. You'll still be able to log into and use YouTube with your account once the deletion is complete.

Summary:
Open YouTube's advanced settings page. Click your profile icon. Select a channel. Scroll down and click Delete channel. Enter your password. Click I want to permanently delete my content. Check the "The following will be permanently deleted" box. Click DELETE MY CONTENT. Enter your channel name or email address when prompted. Click DELETE MY CONTENT.