NOTE (JULY 20, 2013): Check out our guide to installing Lion on an AMD Hackintosh.
Installing Mac OS X on a Hackintosh with an Intel processor well always be easier, but switching from an Intel processor to an AMD processor is extremely inconvenient. If you're interested in attempting an AMD install rather than making a inconvenient (and expensive) switch to Intel, read on.
The problem with AMD Hackintoshes lies in the Mac OS X kernel. The kernel is a critical file that lets applications in Mac OS X communicate with the hardware of your Hackintosh. However, the standard kernel (known as the "vanilla" kernel) is only designed to support Intel processors.
To run Mac OS X on an AMD Hackintosh, you need a legacy kernel, which is a modified version of the vanilla kernel that works with AMD processors. Legacy kernels are version-specific; every version of Mac OS X has its own legacy kernel. For example, the legacy kernel for Mac OS X 10.6.7 won't work on Mac OS X 10.6.8.
Unfortunately, there is no legacy kernel for Mac OS X Lion. Development of the legacy kernel is done almost entirely by one guy, nawcom. Lately, nawcom has put all of his work on hold due to medical problems, so don't anticipate the release of a Lion legacy kernel anytime soon. If you want to install Mac OS X on an AMD Hackintosh, it will have to be Mac OS X Snow Leopard.
The standard iBoot+Multibeast method for installing Mac OS X Snow Leopard on an Intel Hackintosh still works (more or less) for an AMD Hackintosh. The only difference is that you have to use iBoot Legacy, instead of iBoot, to start the Snow Leopard installation DVD. iBoot Legacy is a version of iBoot that contains the legacy kernel. Once you have completed the standard installation process with iBoot Legacy, you need to install the legacy kernel along with Multibeast (you can find the legacy kernel for your version of Mac OS X on Google).
Another common variation of the standard method is to use nawcom's ModCD, instead of iBoot. ModCD is a boot CD that modifies parts of the retail Mac OS X Snow Leopard DVD so that you can apply custom Hackintosh tweaks from within the Mac installer itself. From ModCD, you can install the legacy kernel along with the rest of Mac OS X, by using the "Customize" option available in the last page of the Mac OS X installer.
Finally, the last option for installing Mac OS X on an AMD Hackintosh is to use a Mac OS X "distro". Distros are copies of Mac OS X that has been modified to work with Hackintoshes, including AMD Hackintoshes.
Discussion of distros is prohibited on tonymacx86 and discouraged on several other Hackintoshing sites, because... well, it's illegal. Distros are essentially pirated copies of Mac OS X (with minor modifications for Hackintoshes, of course). The best way to download a distro is to find a copy on ThePirateBay, Demonoid, or some other bittorrent website. The three most popular Snow Leopard distros are: Hazard, iAtkos, and SnowLeoDVD.
Distros are available as ISO files (disc image files). Once you've obtained a copy of a distro, burn the ISO file onto a DVD with ImgBurn, or with the built-in Windows 7 disc burning tool. From there, the installation process is relatively straightforward. Distros have been modified so that they can boot the Mac OS X installer without the need for a boot CD like iBoot or nawcom's ModCD. More importantly, distros permit you to install extra, Hackintosh-specific drivers in Mac OS X during the Mac OS X installation itself, by using the "Customize" option available in the last page of the Mac OS X installer (much like nawcom's ModCD). For AMD Hackintoshes, you need to install the legacy kernel and the AMD Patch.
Of course, keep in mind that support for AMD Hackintoshes is sparse, and in some cases nonexistent. Once you've installed Mac OS X on your AMD computer, whether with iBoot Legacy, nawcom's ModCD, or a distro, you're on your own.