button "go out"

need to make it look exactly like a button, rather than as a sign

Maybe something like this in the header widget?

<a class="button" href="http://google.com">This is a button</a>

how to add a rule to the buttons in the header

added to the widget: <a class="button" href="http://site.com/login.php?action=logout"> Выйти </a>, but now does constantly asks for confirmation exit from the site.

help Tom

Hi there,

Different timezones - I have to sleep some time ;)

Not sure why it would ask confirmation - you must have a plugin or script that asks permission when leaving the site? HTML doesn't have this by default, especially the little snippet I provided.

Also, if you're using WordPress, you may need to change it to this:

<a class="button" href="http://site.com/wp-login.php?action=logout"> Выйти </a>

I'm looking for that too
Is there a simple way to add logout link to one of my menus?
The plugin you suggested: https://wordpress.org/plugins/baw-login-logout-menu/ is too old, haven't updated for a year
Is there a way to use a shortcode maybe?
I'm looking for an answer and haven't found yet...

You can do it with a function if you don't want to use the plugin.

For example, see the answer to this question: http://wordpress.stackexchange.com/questions/156217/add-logout-link-to-navigation-menu

No it doesn't work

I need more information than that to help. What didn't work? Does the menu item not show up? Does clicking the link not do anything?