If your iPhone, iPad, or iPod Touch is running iOS 5 or higher, you can now receive software updates over the air. What this means, to you, is that you'll no longer have to tether to a computer to download and install the update. Instead, you'll be alerted on your device of an available update. You can then can download and install it while on the go. Here's how it works.
To check for an available update, to go Settings > General > Software Update.
If an update is available, you'll see a screen similar to that above. Here you can see software update iOS 5.1.1 is available, and it's 54.5MB. The general notes don't really tell the whole story of what's included in the update, so make sure to tap on Learn More to see what exactly is included.
Some words to the wise: make sure iCloud has a current backup of your device; should anything go wrong during the update process, you'll need to restore to a recent backup. You can watch this video covering how to manually start an iCloud backup. Once you're ready to update, tap on Download and Install.
You'll have to accept some terms and conditions before the download will start. You'll also be prompted to plug your device in to ensure enough battery to complete the download and installation of the update.
You can then view the download progress of the update. You don't have to stay on this screen while the update is downloaded. You can continue to use your device while the download is completed.
Once the download has completed, a pop-up will appear asking if you'd like to install the update now, or delay it. If you don't respond to the pop-up, the update will automatically be applied to your device.
Your screen will then turn black, with only the Apple logo and a progress bar being present. Once the update is applied and has finished, your device will reboot and you'll be back in business.