Prerequisites
To run ReplicatorG, you'll need to have Java 1.5 or later installed. You can download Java from Oracle's download site.
If you want to use the integrated Skeinforge support to generate toolpaths, you'll need to install Python as well. (If you don't know what that means, then go ahead and install Python! It will make your life much easier.) You'll want Python 2.6. Download it from python.org, and follow the installation instructions.
Download
Make sure you've downloaded the latest version of the ReplicatorG software.
Copy folder
Unzip the folder you downloaded and put it wherever is convenient for you.
Install Drivers
The /drivers folder contains drivers for the FTDI USB -> Serial converter chips that the Arduino / Sanguino boards use. If you've already installed Arduino, you can skip this step. Otherwise, follow the instructions on the Arduino website.
Run it!
You can run the application by double clicking the ReplicatorG application.
Done!
Next, move on to the usage page for instructions on configuring and using ReplicatorG.