If for some reason you don’t want to update your Galaxy s3 through Kies Air you can always use the bundled software from the phones manufacturer to get it done. As an excample you might not have access to Wi-Fi or you might not be on a dataplan with your carrier. Another reason for doing this is that this will be the fastest way to get access to the latest version of official Android Os to your phone.
Samsung Kies software
When trying to update my Galaxy s3 to Jelly Bean I could not get it through Kies air, but once I connected my cell phone to Kies I got it immediately.
Backup your data before updating
Even though I have never lost any data when updating my phones, to cover my back I would like to recomend that you do so for safe measure. ( most phone manufacturers recomend that you do ).
Connect your phone to your computer with a micro usb cable. (comes bundled with your phone )
Start Kies on your Pc or mac.
Once Kies connects to your phone it will automatically check for the latest Android Os version for your phone.
If nothing happens : Pull down the notification area on your phone. If you can see that it says connected as a camera, press that area to change your USB options. Pick the connect as Media device.
All that is left for you to do is follow the instructions supplied by Kies. In about 10 minutes or so you should be done. This depends on you network connection though.
You are now ready to take full advantage of the freshest Android version. You can read about it on the Official Android page.
Always keep your phone updated to the latest version to get the most out of your phone. Among the advantages are that you and your data will be safer and that the latest performance improvements will make your phone the best it can be.