Navegar entre dos pantallas

Con Navigator podemos trasladarnos a otra pantalla (Navigator.push) y después regresar a la pantalla inicial (Navigator.pop).

import 'package:flutter/material.dart';

void main() {
  runApp(MaterialApp(
    title: 'Navigation Basics',
    home: Home(),
  ));
}

class Home extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Primera Pantalla'),
      ),
      body: Center(
        child: RaisedButton(
          child: Text('Ir a Pantalla 2'),
          onPressed: () {
            Navigator.push(
              context,
              MaterialPageRoute(builder: (context) => PantallaDos()),
            );
          },
        ),
      ),
    );
  }
}

class PantallaDos extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Pantalla 2"),
      ),
      body: Center(
        child: RaisedButton(
          onPressed: () {
            Navigator.pop(context);
          },
          child: Text('Volver!'),
        ),
      ),
    );
  }
}

Fuente: Navigate to a new screen and back.