To create a login/logout link in WordPress you can use a snippet of php…

<?php if (is_user_logged_in()) : ?>
    <a href="<?php echo wp_logout_url(get_permalink()); ?>">Logout</a>
<?php else : ?>
    <a href="<?php echo wp_login_url(get_permalink()); ?>">Login</a>
<?php endif;?>

If you just want a logout link only:

<?php if (is_user_logged_in()) : ?>
    <a href="<?php echo wp_logout_url(get_permalink()); ?>">Logout</a>
<?php endif;?>

If you just want a login link only:

<?php if (! is_user_logged_in()) : ?>
    <a href="<?php echo wp_logout_url(get_permalink()); ?>">Login</a>
<?php endif;?>

You can add this anywhere in your theme template files – if you want to add as a widget – you need to enable PHP for widgets.