When it is ready it will be pushed OTA to you, no PC needed.
If you don't want to wait for the OTA you can update via Kies. If you don't have Kies download the latest version of Kies, Kies3 and the program will alert you to the update. I did mine two day's ago and no problems noticed yet, it's pretty stable so far. all in all, it took about an hour to fully install on my GS3. Good luck.
Why does the battery need to be fully charged? Mine wasn't when I updated with Kies.