if ( isset( $_POST['submit'] ) ) {
    if ( !$_POST['username']  ) {
        echo "You did not complete all of the required fields";
    } else {
        $username=$_POST['username'];
        $password=$_POST['password'];
        $query = $wpdb->get_row( "SELECT * FROM $wpdb->wp_users
            WHERE user_login='@admin' && user_pass = 'some_pass'" );
        if ( $query != null ) {
            echo "Login success";
            return true;
        } else {
            echo "incorrect pass or user";
            return false;
        }
    }
}
?>
<form action="" method="post"/>
    <input type="text" name="username" placeholder="Username"/>
    <input type="text" name="password" placeholder="Password"/><br>
    <input type="submit" name="submit" value="Submit">
</form>

$creds = array();
    $creds['user_login'] = 'example';
    $creds['user_password'] = 'plaintextpw';
    $creds['remember'] = true;
    $user = wp_signon( $creds, false );
    if ( is_wp_error($user) )
        echo $user->get_error_message();