I have an iPhone. I want to back stuff up. I understand that there’s some iCloud thing out there.
How does it work?
It’s probably already doing it automatically.
On iOS6, Settings->iCloud. Turn on the things that you want to back up. Depending on what you want to back-up, it may ask you to set up an @me account which is free and easy to do. Next go to “Storage & Backup” at the bottom of the screen. Turn “iCloud Backup” on. If it is already on, go to the bottom of the screen to see the last time it was backed up.
I think iCloud uses your iTunes account. Its functions are:
Backup:
Mail (only for @icloud.com addresses)
Contacts
Calendars
Reminders
Safari
Notes
Passbook
Photo stream
Documents and data
So far, I find its use as backup limited, as you can’t restore individual items, only the entire phone.
Another function is to sync items, e.g. photos, reminders, between devices.
The last function is Find My iPhone, to locate and wipe your iPhone if it gets lost.
Another thing you can do with iCloud, although you have to pay, is iTunes Match. That stores all your music on the cloud, and matches it with high-quality iTunes files where available. You can then download or stream it to your phone or another computer, without having to fill your phone memory up with your entire library.
“iCloud” is Apple’s marketing name for a bunch of different things. Email (yourname@icloud.com), data syncing, and backups are the big three. (I also think of the music sync service, iTunes Match, as part of iCloud but I think it’s marketed separately).
This is mostly a list of stuff that is sync’d. For instance, if I have Notes turned on and I write a note on my iPhone, it also shows up on my iPad. “Documents and data” is the catch all for “all the non-built-in apps that know how to sync data” and these apps can be individually controlled.
The data-syncing is independent of iCloud backups, however. Backups are full system backups (or, at least, as full as iOS backups ever are) that are saved in iCloud. If you have backups turned on and get a new device, you can restore everything from your old device to the new device right over the Internet. It’s cool.
Apple has a support article about how exactly iCloud backups work at http://support.apple.com/kb/HT4859. You can read that for full details, but the list of backed up items are:
[ul]
[li]Photos and Videos (in the Camera Roll)[/li][li]Device Settings[/li][li]App Data[/li][li]Home Screen and App Organization[/li][li]Messages[/li][li]Ringtones[/li][/ul]
Note that the apps themselves aren’t part of the backup; but that’s okay because they can be re-downloaded from the App Store.
Backups are serious business, so I definitely recommend reading Apple’s article for yourself to make sure you know exactly what’s going to happen.
I’m unsure about App Data on that list, because after I had a system crash on my iPod Touch it cleared all my game progress even after a back-up, so I had to go through Angry Birds all over again. 
That was pre-iCloud, though, so things may be different these days.
In my defense, I pulled it straight from Apple’s list. 
To clarify, though, “App Data” specifically refer to “application-specific folders that are not a cache or temp directory”. So, app developers have options about where to store their data so that it either is or isn’t backed up. (App developers are encouraged, for instance, to put easily-redownloadable data in folders that won’t get backed up to keep the size of the backups down.)
Theoretically, a user shouldn’t have to care about any of that…until they restore from backup and find out that they have to replay all of Angry Birds again. At which point, you have something to yell at Rovio about, I suppose.
For the sake of anecdote, I can report that I got a replacement iPad last weekend and had to do a restore: all of my app data came over flawlessly. Stuff that I didn’t expect to be saved was there just where I left it.
I was impressed.
If you want to backup iPhone to iCloud, do the following:
Go to Settings>General>Reset>Erase All Content & Settings
Go through the setup assistant again as you did when your phone was new. During this process you will be given the option to Restore from iCloud Backup (see image below). Select this.
Connect your phone to your wall charger and make sure it is connected to wi-fi and let it restore. Be patient as sometimes restoring from an iCloud backup can take hours to complete.