The beta of iOS 7 has been out in the world for a whole week and a bit now; the catch is that you're meant to have a paid-for developer account to install it. This being the internet, though, some intrepid people have found a way round that little bugbear.
Before you dive on in, you should recognise that this is probably illegal (or at the very least, in breach of Apple's iOS Developer PLA). Moreover, iOS 7 beta is very much not ready for public release -- through our testing (with a developer account, I hasten to add), we've found that the OS is stable enough, but a fair few third-party apps crash on occasion. Still, your funeral and all.
There are a few things you need for this to work. First-off, you'll need an iPhone 4, 4s or 5 (or the latest-gen iPod Touch) for this to work. Sorry, no iPad version yet. Next, you'll need a copy of the iOS 7 beta edition. If you're a developer, you can get them in the Downloads section of Apple's website, or for everyone else, there are sites that host the files. You'll want the file that specifically matches your model of iPhone -- there should be a model designation on the back, something like "A4372", which you'll also see in the filename of the iOS 7 beta you want.
Next, you'll want to back everything on your device up. This is pretty easily done, via iTunes or iCloud. Once the device is backed up, plug it into your computer, and hit 'Restore' in iTunes. This should restore it back to a factory version of iOS 6.1.x, with none of your details on it -- when you turn the iPhone on, it'll have the initial set-up screen on.
Once that's done, you simply plug your device back into the computer, and click *Update* (not Restore) while holding down Shift (or Option on a Mac). Navigate to the iOS 7 beta you downloaded, and Bob's your uncle. Once the update to iOS 7 is done (which should take 10-20 minutes, give or take) your iPhone will boot up into iOS 7. Go through the settings, doing everything as you want, but probably turn off Diagnostics Logging to Apple. You don't want this handset phoning home. Once you've done the setup, you should get into iOS 7, and the world is your (much more flat) oyster.
In the (unlikely) event that this doesn't work, what will happen is what should happen when a device not registered with the Developer programme installs iOS 7: Once you come to the end of the initial device set-up, the phone will tell you that it's not registered with the Developer programme, and you'll be stuck.
If you haven't followed the guide correctly (or just want to go back), there is a way to get back to iOS 6: turn your phone off, then hold down the home button while plugging the cable into the iPhone. It'll go into Restore mode, and in iTunes will appear the option to restore your iPhone back. If you need the restore files for any reason, they can be found here.