Caution: I am not liable if you screw up the process for your device or if you need to un-root it for whatever reason. Follow these steps carefully! Make sure to do some research first before rooting your device: make sure that it is important enough to risk voiding warranty.
Step 1: First things first...
Step 2: The App
Step 3: Get the drivers
Step 4: Get the Root files
Now, plug in your phone to the computer via USB. In the USB settings set it to charge only, that seems to help with reliability. The computer might say "installing device drivers". Let that finish.