There are (literally) thousands of free email service providers. I'd recommend choosing a service which can be accessed either through a web browser or by using a proper email client (such as Outlook, Outlook Express, Windows Live Mail, Windows 8 Mail or Thunderbird). The best known of those (as suggested by Sandy) is Google's Gmail:
http://mail.google.com/?hl=en
(Just click 'Create an Account', at the top right corner, and follow the instructions).
However my own preference is to use the excellent service provided by GMX:
http://www.gmx.co.uk/
(Simply click 'Get your free GMX account', at the top of the screen).
Chris