Simple code using the built in WP function that checks if you a user is logged into WordPress.

wp-check-if-user-is-logged-in.php

<?php 
if ( is_user_logged_in() ) {
  echo 'Welcome, logged in user. <a href="'.wp_logout_url().'">Click here to logout</a>.';
}else{
  echo 'Please login by <a href="'.wp_login_url().'">clicking here</a>.'
}