1- Make sure Drivers are Installed for I9003 (Download and install Samsung Kies from samsung website)
2-In Settings--Wireless & Networks--USB setting--select Ask On Connection
3-CHECK USB debugging mode in settings---applications--Development
Go To http://forum.xda-developers.com/showthread.php?t=803682 and download and install SuperOneclick on ur computer
Just plug in the device with your computer, launch Superoneclick, Click "root" tab and Its Done!!
I tried using z4root but it does not work for Samsung Galaxy SL GT I9003
SuperOneClick does work!!