Read this carefully

ROOT METHOD INSTRUCTION :

(1) Download Samsung Kies [google search] and install it. But don't Open it.
(2) enable "USB DEBUGGING" 
from (Menu\Settings\Applications\Development)
(3) enable "UNKNOWN SOURCES"
from (Menu\Settings\Applications)
(4) [OPTIONAL] increase screen timeout to 10 minutes
(5) connect USB cable to PHONE and then connect to PC

For general discussions, bug reports and FAQ, go                                                                     

What's working:

Audio
Receiving and making calls
GPS
Compass
Proximity sensor
Wifi
Bluetooth
USB mass storage
HW accelerated gui
HW accelerated video
Camera
Torch
Wifi/USB tethering
USB OTG
Vsync

Annoyances:
Green color when taking pictures (saved picture is ok though)

Screenshots

Before you install CM-10.1: Preparation (First three are optional. If you want to start fresh, these can be skipped)

1. Install AppBak from Market, run it and save a list of all your apps.
2. Install SMS Backup and Restore from Market, run it and backup your SMS history.
3. Install Call Logs Backup and Restore from Market, run it and backup your call log history.
4. Boot into CWM5 recovery. Make a full backup. You will need this backup later if you decide to go back to your previous ROM and data.

WARNING: Many apps will Force Close crash if you restore data from a previous ROM.

Install

  *  Use CWM5 or CWM6.                 

• Warning: Only use this recovery to flash CM-10.1. Otherwise, you risk bricking your phone!

1. Wipe data and cache.
2. Flash update*.zip.
3. Flash gapps*.zip. You must flash gapps after every upgrade to CM10.1 since /system is formatted, wiping your previous add-ons.
4. Reboot phone.
5. After you setup your Google account, reinstall the three apps from Market in order to restore most of your apps, call log and SMS history.
6. Warning: Do not restore backup data of system apps!
   • If you restore a bad backup with cached settings in telephony.db in data/data/com.*.*.telephony it can break MMS.
   • It seems that restoring backups can also break Calendar sync.

Upgrades
Upgrades from previous versions of CM10.1 are the same process as install, except you do not need to wipe anything. Contrary to popular belief, you do not need to even wipe cache and dalvik-cache when upgrading between CM10.1 versions. You only need to wipe if you are doing a major upgrade, switching to a different ROM entirely, or attempting to fix bugs caused by bad backups or corrupt app data.