The key function to use is wp_logout_url
. This function returns the URL for a user to logout.
You can construct a regular anchor tag / link markup around it and style that as you see fit.
wp_logout_url
takes an optional $redirect
argument to send the user to after logout. Here’s a sample with markup and the TLD as redirect:
echo '<a class="button" title="Log me out" href="' .
wp_logout_url( get_bloginfo('url') ) .
">Logout</a>';