If you're ready to break up with Yahoo Mail after the company's massive breach (seriously, basically every user has been hit) here's a quickie guide on how to make the switch.
1. Go to the "Terminating your Yahoo account" page. (If you use a phone number to sign in, go to the "alternative account termination page" instead.)
2. Read the information about deleting your account to be sure you want to proceed.
3. Enter your password.
4. Click the button labeled "Yes, terminate this account."
Now before you officially call it quits, remember that when you delete your Yahoo account, you also lose access to Yahoo related sites like Flickr and the fantasy sports leagues.
So, if you have any important contacts, photos, mail, rosters, etc. save what you need and transfer what you can.
If you want to change to a less problematic mail service, CNET gives the lowdown on how to transfer your mail to Gmail:
Once you've signed up for a Gmail account, go to the inbox and click the gear-icon button in the upper-right corner and click Settings.
Next, click Accounts and Import at the top of the page and then click Import mail and contacts.
Here, you can enter your Yahoo email address and import your Yahoo data to Gmail. You can choose to import contacts, mail and new mail for the next 30 days.