How to root the Samsung Vibrant SGH-T959 (Galaxy S)

The general procedure for rooting a Samsung Vibrant (Galaxy S) on t-mobile has been posted by others (basically restating justadude's xda forum post). However, those posts are missing some details, especially if you've never rooted an Android before; I've added explanatory notes below.

[update] A new XDA thread makes it even easier.


How to root the Vibrant

1. Download the root (superuser, SU) package and rename it to update.zip
• Note: you may need to name the file update instead of "update.zip".
2. On your device, navigate to Settings : Applications : USB settings, and select Mass storage.
• On Mac OS X or Linux, you may also need to enable Settings : Applications : Development : USB debugging.
3. Plug your device into your computer, select Mount USB from your device’s pull-down window.
4. Copy the update.zip to the internal SD directory (the ~14gb drive, not the ~2gb SD card).
• This is the top level--not a subdirectory--of the 14gb drive (appears as E: in Windows). On the Android filesystem, the actual path will be /sdcard/update.zip
5. Turn the phone off.
• If the USB cable is plugged into a computer, unplug it. Otherwise an interminable "Downloading..." screen will appear in the next step.
6. Hold down volume up and volume down while powering on the phone; the recovery menu should appear.
• Try holding volume-up with your left thumb, volume-down with your right thumb, then press the power button with your right index finger.
• Let go of the power button when you see the "Vibrant" start screen, or it might keep rebooting.
7. In Recovery menu select "Reinstall Packages" (use volume-down, then power to select).
• At this point, if you see this error:
  
  
  E: Can’t open /sdcard/update.zip
  (No such file or directory)
  Installation aborted.
  
  
  The path /sdcard/ refers to what you saw as the top level of your E: drive when you mounted your phone in Windows. Go back to step 1 or 4 and make sure update or update.zip is in the right place on your phone.

Once "Reinstall Packages" has run update.zip correctly, your phone is now rooted. Now you can mess with the filesystem to your heart's content (e.g., delete Avatar.apk and Avatar.odex from /system/apps).

If you find that /system is mounted read-only, try this¹ as root:
mount -o rw,remount yaffs2 /system

After deleting a .apk/.odex package via rm, you may need to also:
pm uninstall <package_name>

To mount system ro again:
mount -o remount,ro /system

Going further...
Now that your phone is rooted, you may want to update the Superuser package to the latest version, which has many improvements.

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How to un-root (that is, reverse the steps performed by update.zip)

Rooting may void your warranty or support with your carrier. In that case you might want to reverse the process. Here's how:

Note: this is only a partial reversal.

$ su
# rm -r /system/app/Superuser.apk
# rm -r /system/bin/su
# rm -r /system/xbin/su
# rm -r /system/xbin/busybox
# reboot

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[1] I assume you have installed a terminal app, and that you are familiar with the command line.