simply render the log in from in wordpress is so simple:
<?php wp_login_form( $args ); ?>
Here is $args
definition :
<?php $args = array( 'echo' => true, 'redirect' => site_url( $_SERVER['REQUEST_URI'] ), 'form_id' => 'loginform', 'label_username' => __( 'Username' ), 'label_password' => __( 'Password' ), 'label_remember' => __( 'Remember Me' ), 'label_log_in' => __( 'Log In' ), 'id_username' => 'user_login', 'id_password' => 'user_pass', 'id_remember' => 'rememberme', 'id_submit' => 'wp-submit', 'remember' => true, 'value_username' => NULL, 'value_remember' => false ); ?>