The Samsung Galaxy S4 is finally on sale and many users will be looking to make it do things Samsung would rather it didn't. The Samsung Galaxy S4 has been rooted which will allow you to install custom ROMs, different modifications to its user interface as well as add many new features that can only be achieved by rooting the smartphone. This root guide will work on the AT&T, Sprint, T-Mobile, and Verizon Samsung Galaxy S4 in the U.S. and any other region that receives the Galaxy S4 with the 1.9GHz Snapdragon processor. This process is one of the easiest ways to root an Android device; it only takes a few steps to achieve. Here's how you'll go about rooting your shiny new Samsung Galaxy S4.
You'll first need to download the zip file found here.
1. Extract the entire contents of the zip file.
2. If you are using Windows, ensure you have installed the latest Samsung USB drivers available for your phone.
3. Ensure USB Debugging mode is enabled on your device.
4. Connect your device to your PC via USB.
5. If you are using Windows, navigate to the extracted directory and execute "run.bat". If you are using Linux or OS X, navigate to the extracted directory in a terminal and execute "./run.sh".
6. Approve the ADB connection from your PC on your device.
Once the process is complete your Samsung Galaxy S4 will be rooted and while there aren't too many custom ROMs for the Galaxy S4 yet (it literally just came out), that number will be growing very fast.
Special thanks to djrbliss over at XDA for putting this program and guide together.