If you're actually using Internet Explorer (rather than the Windows 8 Mail App) the procedure should be the same as on a PC. i.e. click the down arrow next to your email address in the upper-right-hand corner and select 'Sign out'.
If you're using the Windows 8 Mail App the answer is simple: You can't!
(Microsoft designed Windows 8 on the assumption that each user of a device would have their own log-on and that they'd password protect devices such as phones, so users remain logged onto any email account unless they actually remove it. Unsurprisingly there have been rather a lot of complaints!)