Before you read this answer, please understand rooting your phone will cancel your warranty. (although all 4 of my Android phones are rooted and running CyanogenMod7 [android 2.3.4]).
There is NOT a one click rooting process for your phone so you will need to type in many commands yourself. Here is the process to follow.
Download and Install Samsung Drivers
64bit:
Download Samsung Galaxy S USB Driver for Windows x64 Driver for Windows XP X64 / Windows Vista64 / Windows 7 x64 - Softpedia
32bit:
Download Samsung Galaxy S USB Driver for Windows x86 Driver for Windows XP / Windows Vista / Windows 7 - Softpedia
Download and Install ADB
Android SDK | Android Developers
Android SDK | Android Developers
Download the attached files
Setup ADB to work in your PATH
Windows: Go to System Properties > Advanced Tab > Environment Variables
Click on the Path variable under System Variables and hit edit
Add a colon: and the location of your android-sdk tools folder
In example :C:\Android\SDK\android-sdk-windows\tools
connect your phone with the usb cable and go to settings > applications > enable debugging
run cmd
cd to the directory of the unzipped files included and follow these commands to a tee
adb push su /sdcard/su
adb push rage.bin /data/local/tmp/rage.bin
adb push busybox /sdcard/busybox
adb shell
cd /data/local/tmp
chmod 0755 rage.bin
./rage.bin
wait....
when it brings you back to your original shell or windows cmd promt follow these commands
adb shell
mount -t rfs -o remount,rw /dev/block/stl9 /system
cd /system/xbin
cat /sdcard/su > su
cat /sdcard/busybox > busybox
chmod 4755 su
chmod 4755 busybox
exit
adb install Superuser.apk
Thats it, I hope this helps you. Its a complete rooting process.
Once you have Root, simply download ROMManager from the Market, do a "Backup" from the app, and download whichever ROM you want from the list of available ROMs inside the app, enjoy!
Read more: how to root android 2.1 on Samsung Gem - JustAnswer
how to root android 2.1 on Samsung Gem - JustAnswer
