Good information fastlerner, I would just like to add an alternative method that worked for me for installing the superuser app and clockworkmod recovery(version 18.104.22.168) from jt1134 - file name is cwm4-bml-i500.tar - on the cyanogenmod wiki for the showcase i.e. Rooting your phone. You might need to disable any antivirus software on your computer and/or phone for Odin to work properly.
1. Do your homework, research the pros/cons of installing a custom recovery on your phone and carrier. It can result in software damage to your phone if done improperly, which may or may not be repairable.
2. If you decide its worth it, search for and download all the necessary drivers for your phone if you dont have them already. Windows usually verifies this automatically when your plug the phone in with the data cable. If it recognizes the phone and you can mount sd card and view files on it, then you most likely have the drivers.
3. Search for and download superuser (the file I used was su-22.214.171.124.x) and the program Odin(i used version 1.7).
4. On your galaxy go to settings, applications, development and check enable USB debugging.
5. Connect your galaxy to your computer with the USB data cable and mount sd storage (to allow file exchange between phone and computer, just like you would do to copy pictures from your phone).
6. Copy the superuser file(su-126.96.36.199.x), downloaded earlier, to the root directory of the sd card and not inside any folder.
7. Tap unmount sd card on phone then unplug the data cable from the phone and not the computer you will need it soon.
8. Turn the phone off and pull the battery out.
9. Install Odin to windows if you didnt after it downloaded and open it up and click the PDA button to open the clockworkmod recovery file(cwm4-bml-i500.tar) you downloaded from the wiki.
10. Leave all options unchecked in Odin.
11. While holding the volume down button on the phone, insert the data cable. When you see the yellow, android downloading screen appear release the volume down
12. You are now in download mode and Odin should recognize the phone in one of the white boxes ID:COM
13. Re-insert the battery and click start in Odin.
14. Once the install completes Odin will say pass and the phone should shut off.
15. To launch the new cwm recovery, hold both volume up and while holding them down press and hold the power on button until you see the samsung logo boot.
16. Inside the recovery you will see the option to install zip from sd card, volume down will take you there, power button will select it.
17. Next, select choose zip from sd card
18. Select to install the superuser zip file(su-188.8.131.52.x) you put on the sd card earlier.
19. When its done go back until you see reboot system now.
Youre all set. Now you can use apps that are for root only users, flash new roms such as cyanogenmod 7, and perform nandroid back ups.
Edited by rbriggins, 19 January 2012 - 08:16 AM.