Right now, are you looking at the list of messages in your Inbox, or are you actually reading a message?

If you’re looking at your list of messages:

Click in the checkbox to the left of the message you’d like to delete. Then click Delete at either the top or bottom of the list of messages. This will send the email to the Trash folder.

While you're reading a single message:

Click Delete at either the top or the bottom of the message. This will send the email to the Trash folder.

To permanently remove the contents of Trash, click Empty next to the trash folder on the left side of the page. “Are you sure you want to empty this folder?” If so, click Empty to delete... or Don’t Empty if you’d rather not. When messages are emptied from the trash folder, they are permanently deleted from the Yahoo! Mail server and cannot be recovered.