How to pass data from child widget to its parent

The first possibility is to pass a callback into your child, and the second is to use the of pattern for your stateful widget. See below.

import 'package:flutter/material.dart';

class MyStatefulWidget extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => new MyStatefulWidgetState();

  // note: updated as context.ancestorStateOfType is now deprecated
  static MyStatefulWidgetState of(BuildContext context) =>
    context.findAncestorStateOfType<MyStatefulWidgetState>();
}

class MyStatefulWidgetState extends State<MyStatefulWidget> {
  String _string = "Not set yet";

  set string(String value) => setState(() => _string = value);

  @override
  Widget build(BuildContext context) {
    return new Column(
      children: <Widget>[
        new Text(_string),
        new MyChildClass(callback: (val) => setState(() => _string = val))
      ],
    );
  }
}

typedef void StringCallback(String val);

class MyChildClass extends StatelessWidget {
  final StringCallback callback;

  MyChildClass({this.callback});

  @override
  Widget build(BuildContext context) {
    return new Column(
      children: <Widget>[
        new FlatButton(
          onPressed: () {
            callback("String from method 1");
          },
          child: new Text("Method 1"),
        ),
        new FlatButton(
          onPressed: () {
            MyStatefulWidget.of(context).string = "String from method 2";
          },
          child: new Text("Method 2"),
        )
      ],
    );
  }
}

void main() => runApp(
  new MaterialApp(
    builder: (context, child) => new SafeArea(child: new Material(color: Colors.white, child: child)),
    home: new MyStatefulWidget(),
  ),
);

There is also the alternative of using an InheritedWidget instead of a StatefulWidget; this is particularly useful if you want your child widgets to rebuild if the parent widget’s data changes and the parent isn’t a direct parent. See the inherited widget documentation