First you're going to need some files:
- Odin - the software used to flash your phone
- Rooted System Image - what Odin flashes onto your phone (large download, also in torrent) MD5=be4350a56e739eaf7a4184352d653a7b
- Boot your phone into Odin Mode and plug your phone into your computer.
- Start Odin, you should see your device in the ID:COM area
- Select PDA and browse to the rooted.system.img.tar file (second one you downloaded)
4. Click "Start" and wait. This process took around 10 minutes for me. Your phone will auto-reboot and Odin will have a large green "PASS!" in the top left. Congratulations, you're rooted!
If all you wanted was root then you're finished at this point; however, if you want to install clockworkmod you'll need to use the adb. You can find instructions on how to set that up here.
Instead of the instructions below, if you want clockworkmod, simply use the awesome (and free) app EZ-Recovery and check out the ROM installation tutorial for how to use it.
cd Desktop cd platform-tools adb.exe adb push recovery.img /sdcard/ adb shell su dd if=/sdcard/recovery.img of=/dev/block/mmcblk0p18 exit exit adb reboot recovery
And, as per usual, a video tutorial: