First go to the yahoo sign in page and click the option “I can’t access my account!”
When you click it you will be routed to the page where you will be asked about “What’s the problem you are experiencing?” with a number of options. Just select the option “My account may have been compromised” and click next.
Now you will be routed to another page "We’ll help you sign in to Yahoo!". Here you will enter your Yahoo Id and captcha code. After you have successfully entered the security code click Next.
On the next page, you will have to enter the information to verify your identity. The information you have already given in the "Yahoo! Account Settings" should be given here as well. If you have given the alternate email address you will be asked to enter it here and your password recovery information will be sent to you on that email account. Otherwise, if you have given your mobile number then you will be sent a reset code through an SMS. Take this code and enter it in the Yahoo Recovery Wizard page and you will be routed to the Reset Password Page, where you will be asked about the recovery questions .
Now you will be taken to the password recovery page where you will be asked to reset your password and then retype it. If both of the fields match then you have successfully reset your password.
Now that you have set the password, you will be asked to change recovery options. And finally after this, you will be routed to your lost email account!