Note: Check out an updated version of this post with iOS 7 and beyond screenshots and instructions.
Apple today released iOS 5.01 - a minor update to iOS 5 that includes:
- Fixes bugs affecting battery life
- Adds Multitasking Gestures for original iPad
- Resolves bugs with Documents in the Cloud
- Improves voice recognition for Australian users using dictation 1
As this is the first time for most people to be able to use over the air (OTA) updating instead of having to update via iTunes, I thought I'd post the steps to do the update. 2 3
Find Settings.app
It has the gear style icon:

General
Scroll down until you see the General section:

Software Update
Assuming you've got 5.0 properly installed you should see a Software Update item:

Checking for Update
The iPhone will ping Apple's servers to see if there's an update:

iOS 5.01 Download and Install
You should see the Download and Install option beneath the description of what's in the update:

Click here to see what's behind the Learn More option
Terms & Conditions
Hooray! T&C. Make sure you run it past your lawyer before you agree to install.

Connect Your iPhone To a Power Source
If you aren't already plugged into something, it prompts you to plug it in:

Download Ahoy!
It took just under 2 minutes to download but your connection speed will vary:

Preparing Update
It took longer to prepare the update than it did to download:

iOS 5.01 Will Be Installed In 7 Seconds
Click install or watch it countdown:

Verifying Update
Depending on how many other Apple nerds are doing it at the same time as you, this could take a few minutes:

Restart and then Restart Again
At this point the visual tour ends as I can't take screenshots while it's restarting and installing. But my iPhone restarted a couple of times with a progress bar both times. After the second restart/progress bar, my iPhone rebooted to a normal screen and was done.
A quick check back into Software Update reveals that iOS 5.0.1 is installed and I'm up to date.

Done.
- Crikey! ↩
- Assuming you're already running iOS 5.0 ↩
- Though this tutorial covers the upgrade on an iPhone 4, the same process works for iPad and iPod touch devices that are compatible with iOS 5 ↩