Here is the video guide & overview of Jelly Bean 4.1:

Useful links:
–XDA post by Faryaab
–Direct Download link

Here is the written guide to flash 4.1 Jelly Bean on the GT-I9300:
-Have your phone rooted, and CWM installed – Click here – for a guide on that
-Have a CUSTOM ROM or ODIN ready to flash after trying 4.1 Jelly Bean – I highly suggest having a custom ROM on your INTERNAL SD card (such as Omega ROM) – read the note below for more info
-Download the ROM
-Put .zip file of the ROM into your internal SD card
-Turn off phone
-Get into recovery
-Wipe data/factory reset
-Wipe Cache
-Wipe Dalvik Cache
-Choose to flash using internal sd card
-Flash
-Reboot
-Wait for boot
-Enjoy your Jelly Beans!

A note: You won’t be able to access your INTERNAL nor EXTERNAL SD card, through the phone, nor through the PC, whilst being on 4.1 Jelly Bean – however, if you go back into CWM (yes it isn’t wiped) you can flash a custom ROM and/or flash via ODIN (download mode). I highly doubt anyone will want to be on 4.1 on the SGS3 for the time being, as you can literally do nothing, thus to get back to a normal ROM, just flash another one via CWM (that’s what I highly recommend as it’s fast and easy to do so)

Here are the pictures:

As of the 29/06/2012 – what works and doesn’t (by Faryaab):
What Works:
ADB
Touchscreen
Hardware Acceleration
Notification LED
Cellular Rado (But No Audio so no Calls)
Physical Buttons
SMS
Accelerometer
Charging
Maybe More

What Doesn’t work:
Wi-Fi/Bluetooth/NFC
Audio
Camera
MTP
Storage
Maybe more

May the Bean of the Jelly be with you!
–TotallydubbedHD