Create flutter project with `flutter create` and replace the source file with this

main.dart

import 'package:flutter/material.dart';

class MyKeys {
  static final GlobalKey navKey = GlobalKey<NavigatorState>(debugLabel: 'navKey');
}

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      routes: {
        "/": (_) => MyHomePage(key: MyKeys.navKey, title: 'Home Page'),
        '/auth': (_) => MyAuth(),
      },
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

  final String title;

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _counter = 0;

  void _incrementCounter() {
    setState(() {
      _counter++;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            FlatButton(
              child: Text('Login'),
              onPressed: () => Navigator.of(context).pushNamed('/auth'),
            ),
            Text(
              'You have pushed the button this many times:',
            ),
            Text(
              '$_counter',
              style: Theme.of(context).textTheme.display1,
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: _incrementCounter,
        tooltip: 'Increment',
        child: Icon(Icons.add),
      ),
    );
  }
}

class MyAuth extends StatefulWidget {
  @override
  _MyAuthState createState() => _MyAuthState();
}

class _MyAuthState extends State<MyAuth> {
  String login;
  String password;
  final _formKey = GlobalKey<FormState>();

  void _doLogin() {
    final form = _formKey.currentState;
    if(form.validate()) {
      form.save();
      Navigator.of(context).pushNamed('/');
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('Login')),
      body: Padding(
        padding: const EdgeInsets.all(24.0),
        child: Form(
          key: _formKey,
          child: Column(
            children: <Widget>[
              TextFormField(
                decoration: InputDecoration(
                  labelText: 'Enter login',
                ),
                autocorrect: false,
                autofocus: true,
                validator: (v) => v.trim().length < 3 ? 'Enter more than 3 chars': null,
                onSaved: (v) => login = v.trim(),
              ),
              TextFormField(
                decoration: InputDecoration(
                  labelText: 'Enter password',
                ),
                obscureText: true,
                autocorrect: false,
                validator: (v) => v.trim().length < 3 ? 'Password should be no less than 3 chars': null,
                onSaved: (v) => password = v.trim(),
              ),
              FlatButton(
                child: Text('Login'),
                onPressed: () => _doLogin(),
              )
            ],
          ),

        ),
      ),
    );
  }
}