Even here at Network World, I managed to completely bork my work laptop's Windows install and lose a bunch of data while trying to adjust my disk partitions for dual boot. (OK, the IT folks just re-imaged it and made fun of me a little, but still.)
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I've had an HTC One (M7) for well over a year now, and while it's generally been an excellent device, the performance and battery life have started to falter a bit. Also, it reboots itself at strange times, without any apparent prompting. It's just sort of what happens to smartphones over time.
Strangely, however despite the characteristic headaches and data loss I incurred when I rooted the other two Android phones I've owned it went smoothly this time. I credit an increasingly mature community around the software involved, experience, and the fact that my gremlins apparently took the day off.
The root
Essentially, what you're trying to do with the first step in the process is obtain root access to your device -- which you almost certainly don't have by default, if you got it from your carrier and install a recovery image, which is a sort of a mini-operating system that lets you install custom software.
How you root your Android device depends on what model you own be aware that there are often several sub-models of any given device sold under the same brand name, which differ in subtle but important ways. Make sure that any instructions you follow for, say, your Moto X aren't the ones for the T-Mobile version, instead of the AT&T version or the GSM version.
There are multi-device rooting toolkits out there, but your best bet is to find a set of instructions specific to your device if a multi-tool like Kingo Root works, great, just make sure that whatever app or instruction set you use applies to the precise phone or tablet you're working on.
Backup/management
So now you're rooted, congratulations! Who needs warranties, anyway It's time to slap a sweet new operating system on there and get cracking. Oh, wait, no it's not you need a recovery image.
Fortunately, this bit is easy - and the method I use is fairly idiot proof. Once rooted, I just:
TeamWin Recovery Project, or TWRP for short, is also highly regarded, though I haven't tried it.
New ROM!
ROM Manager includes an in-app browser for custom ROMs (software packages) that it can automatically download, but I find that the selection is dated and limited. Fortunately, it's easy to find good alternatives to vanilla Android by yourself. Some popular choices:
Other ROMs are available just make sure you're downloading what you think you're downloading, and stick to well-known options until you've got some experience under your belt.
Google Apps
You might think you're ready to install, but, sad to say, you're not quite there yet. Here's what will happen if you install your cool new ROM right now everything will boot up nicely, you'll get the excitement of a new operating system, and then you'll be very frustrated because your new ROM doesn't include Google's proprietary apps.
And since the Play Store app is part of the package, you won't be able to just go download all the stuff you want as usual.
Instead, before you install, you want to go find a .zip file with the Google Apps package designed for the Android version on which your ROM is based, and install that along with the ROM. There's a very handy guide, along with links to the packages you'll need on DroidViews.com. (Thanks, DroidViews people!)
To install, simply download the ROM designed for your specific hardware onto your phone (it's really important to get the right version!), select "install ROM from SD card" in ROM Manager, and make sure both the backup and the "wipe data and cache" options are selected. Then hit "add zip" and select the Google Apps package.
Now you're ready to install.
A couple caveats
First, any specific instructions that come with any component you're installing here, whether it's a rooting method or a ROM or a recovery image, take precedence over what you've read here. This is what worked for me, your mileage may vary for a vast range of different reasons.
Second, obviously, rooting isn't risk-free if you botch something too badly (though you'd have to try pretty hard these days) you run the risk of turning your phone into a fancy Android-powered paperweight, so be careful and make sure you understand what you're getting yourself into. Just rooting your phone can void your warranty, so that's something else to be aware of.
Other than that, have fun! Having the freedom to tweak and customize your Android device as you see fit is great, and gives you at least five extra points of geek cred.