I decided to update my old iOS upgrade guide with new iOS 7 based screenshots and with iOS 7.1 out (full details on Macrumors.com, Macworld.com or Apple.com), now's as good a chance as any.
Minimum Requirements permalink
First make sure your device meets the compatibility requirements Apple has specified for iOS 7. You can check Apple's website or view the screenshot I've embedded below:
[gallery type="rectangular" link="none" ids="21912"]
Unlike your computer where you might be able to run a new game or app on an older computer that doesn't meet the minimum system requirements and just deal with slower performance or graphics, Apple's iOS updates simply won't install on a device Apple hasn't approved.
It's the gear looking icon. If you can't remember where you put it, try swiping down to use Spotlight and start typing "settings":
Scroll down until you see General
Tap Software Update - which might have a 1 beside it indicating there's an update waiting. Otherwise tap through and it will check for an update.
Checking for Update permalink
Your iOS device will ping Apple's software update servers to see if there's a new version.
iOS 7.1 Download and Install permalink
Tap the Download and Install option to get this party started.
Terms & Conditions permalink
Lawyer speak for "We're not responsible if this breaks your phone because, like, yo."
It'll now begin downloading. Your download size will vary depending on what version of iOS you're upgrading from. In my case I had iOS 7.0? installed so it was a 152MB update.
At this point you can switch away and use your iOS device for other stuff while it's updating. (I got a phone call during my update. Thanks Mastercard!) From my roots in the Microsoft Windows world I'm always sketchy about doing anything else while a software update is happening so your mileage may vary.
After downloading it will prepare the update.
...and then it will continue to prepare...
Install iOS 7.1 Update permalink
Confirm that what you've started you'd like to finish.
Note: Depending on your device and version of iOS that you're upgrading from, it can take a half hour to update. So if you have a meeting in 5 minutes, you may want to do it later.
Verifying the Update permalink
Wait! We need to verify that what we just downloaded is what we want to install. So wait!
Long White Bar of Upgrade Process permalink
Now you wait while your iOS device gets updated.
It took about 30 minutes for me start to finish. Your mileage may vary.
If you navigate back to Settings.app, General and Software Update you should see that you're good to go with iOS 7.1.
How does iOS 7.1 feel on your device? My initial impressions on my iPhone 4 is that it's snappier. We'll see after more extended use.