How to implement a side menu that swipes from the left?

The Stocks example has a somewhat less complicated use of Drawer.

Here is an example for a simple Drawer (I just adapted the default project setup from flutter create):

import 'package:flutter/material.dart';

void main() {
  runApp(new MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      title: 'Flutter Demo',
      home: new MyHomePage(),
    );
  }
}

class MyHomePage extends StatefulWidget {

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

class _MyHomePageState extends State<MyHomePage> {

  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(
        title: new Text('TestProject'),
      ),
      drawer: new Drawer(
        child: new ListView(
          children: <Widget> [
            new DrawerHeader(child: new Text('Header'),),
            new ListTile(
              title: new Text('First Menu Item'),
              onTap: () {},
            ),
            new ListTile(
              title: new Text('Second Menu Item'),
              onTap: () {},
            ),
            new Divider(),
            new ListTile(
              title: new Text('About'),
              onTap: () {},
            ),
          ],
        )
      ),
      body: new Center(
        child: new Text(
          'Center',
        ),
      ),
    );
  }
}

The docs are a good place to start ;)

Btw: including a drawer in your scaffold also takes care of the menu button and the left swipe gesture for you.