The first step to the process is to download the Android app from the google Play Store. It is called ClockworkMod Tether. The app is free for 14 days. Once the 14 days is up, you will be able to purchase the full edition for $4.99. The upgrade is in app only, so you must download the free version first. Why wouldn't you anyways?
Once you have downloaded the app, as you will notice when you open it, you will need to download the app for your computer. It will ask you to open the app on your computer to get started. There is an app as well as a driver that is needed for this. In order to get the driver, you will need to visit clockworkmod.com. You can visit the site from your computer or your phone, which is convenient if you don't already have internet access. You will then need to click tether drivers at the top of the screen. It will take you to a list of makes of phones such as Motorola, Samsung, etc. Obviously, being the Samsung Galaxy s III, you are going to click the samsung drivers link. After it is downloaded, if you are using your computer, simply open the file and install it. If you have downloaded it to your SIII, you will need to connect your phone to your computer, find the file in the folder clockworkmod, and install it.
After everything is installed, you can open the app in your phone and turn on the tethering. After you have done this, open the program (which should also be installes from the clockworkmod folder) and click start. It will configure and it should say connected after a few seconds. Then, open your browser and you should be online!
I just discovered this and so far it is working GREAT! I got booted off once, not really sure what happened. But I turned off the tethering through the app first, then through the computer and restarted it all again and all is good. Hope this helps everyone looking for the answer! I will post again when I discover a way to use hotspot for free with no root.