Getting the Beta
In order to have the beta version of Safari installed, you're going to first need to download the required software. For this article, you will need the second beta of Safari for Leopard, available here, as well as an application called Pacifist, which can be obtained at http://www.charlessoft.com/.
When you've downloaded the software, install Pacifist by copying the folder inside the DMG to your Applications folder. Then mount the Safari DMG and ensure that you have a file called "Safari4.0BetaSecUpdateLeo.pkg" inside. Open Pacifist and then drag this file on top of the open window. Pacifist will then display the contents of the pkg file. Browse to applications and then copy Safari.app to your desktop. When asked if you'd like to use administrator privileges, answer yes if you know them.
Unfortunately, Apple has included some checks to prevent the beta of Safari from running on Snow Leopard. Fortunately for us, these checks are very easy to circumvent. Simply, right-click (control-click for those without a two-button mouse) on the Safari beta application that you just copied and go to "Show Package Contents". Then, browse to the Contents folder. Now go to your Safari program in the Applications folder and do the same thing. Inside the Safari application, you'll notice that there are two files, "info.plist" and "version.plist". Drag and drop those into the Safari beta folder. When asked if you want to replace the files, say yes.