how to install xcode 4.2.1 for OS X Lion 10.7.5

These instructions say "install xcode", but then say "once you have xcode installed". Pardon, didn't they skip a step? How do you install xcode?

2.1.1. Install Xcode on OS X 10.9 or later

Download the latest version of Xcode from the Apple developer website or get it using the Mac App Store.

Once you have Xcode installed, open a terminal, run xcode-select --install, ...

Granted, I'm not running 10.9. Here's my version's instructions:

2.1.4. Install Xcode on older releases of Mac OS X

If you have an earlier release of Mac OS X, you may download the latest version of Xcode for OS X 10.5 (Xcode 3.0 and Xcode 3.1 Developer Tools) or 10.4 (Xcode 2.4.1 and Xcode 2.5 Developer Tools) from the Apple developer website.

Ensure that those of the following options that are available in the installer for your version of Xcode are selected:

UNIX Development
System Tools
X11 SDK
Command Line Support

I downloaded installxcode_421_lion.dmg for this system:

System Software Overview:

  System Version:   Mac OS X 10.7.5 (11G63)
  Kernel Version:   Darwin 11.4.2
  Boot Volume:  Untitled
  Boot Mode:    Normal
  Computer Name:  a MacBook
  User Name:    thufir (thufir)
  Secure Virtual Memory:    Enabled
  64-bit Kernel and Extensions: No
  Time since boot:  7 minutes

I double click the download and install it to Applications? Sorry, this is an alien process.