how to install ios 6 on iphone 4

There are two paths for upgrading your current iPhone to iOS 6: over the air or through iTunes.

If you didn't line up at your local Apple Store or preorder an iPhone 5, you can still upgrade youriPhone,iPad, and iPod Touch to the latest version of iOS released today. I should say it's likely you can upgrade your current device because the new version of Apple's mobile operating system, iOS 6, is compatible with most but not all previous-generation devices.

You have two methods for downloading and installing iOS 6. You can simply update your iOS device over the air via the device's Settings, or you can connect it to your computer and use iTunes.

Method 1: Over the air
The easier of the methods is to grab your iPhone, iPad, or iPod Touch and update wirelessly. Before doing so, however, it's wouldn't be a bad idea to sync your device with iTunes if you haven't done so in a while. There have been instances with past iOS updates where users have reported the new iOS didn't install correctly, bricking their phone and forcing them to restore their phone before trying again. So, if your iOS device has talked to iTunes recently, go ahead and go to Settings > General > Software Update.

You should see iOS 6 listed, with a Download and Install button below it. Tap the button, agree to Apple's terms and conditions, and either heed or ignore Apple's advice to connect your device to a power source during the download to save battery.
After iOS 6 installs, your device will restart, which was a rather lengthy process in my experience (20 minutes or so, after the roughly 45 minutes it took to download and install). After restarting, you'll be greeted by a shiny, new iOS 6 lock screen. Slide to open your device and click through the following four setup screens: