Need to unlink Yahoo from email

I am canceling my verizon service but would like to buy my email address.  I need to unlink my yahoo portal from my email before I cancel my verizon service and would like to save my emails/contacts.  Could you please walk me through what I am supposed to do?  Everytime I try to change my online experience i get bounced back to my account page.  Please let me know how I can unlink yahoo and save my emails/contacts before I cancel my service.  Thanks!