kentaya - before I run you around in circles with my personal reccomendations, I suggest you do a little light reading in the all things root section of this forum; in particular, I recommend ScaryAlien's posts on this subject, as they are very detailed and easy to follow.
This is how I learned about rooting and tooke the jump. Adb is included in the Google SDK development tools, which you can download and install for a Windows PC from here Android SDK | Android Developers
assuming you have a Woindows machine. Just follow the installation instructions and run the latest updates (the UI is fairly simple and only requires a tick in the boxes for the packages you want to update - if in doubt tick them all).
One tip, in order to execute adb shell commands to push/flash images to your phone you'll need to access the 'platform tools' folder in Windows terminal (cmd). In order to be able to do this you have to either type the lengthy and convoluted pathe to the folder location or, better still, navigate to the above-mentioned folder in explorer and press shif and right-click on the folder simultaneously with your mouse upon which you get the drop-down menu where you select 'open command window here' you are now in the right location to start using adb.
You also need to make sure that all your images > bootloader > radio > image-...-.zip and last but not least a custom recovery, are all located in the platform tools folder.
The stuff you need to enable communication between oyur PC and your phone are the correct drivers; just google Samsung Nexus S Windows drivers from here http://drivers.softpedia.com/progDownload/SAMSUNG-USB-Driver-1480-Download-141878.html
. Download and install them and hook up your Nexus. Be warned this is the only tricky operation in the whole process, getting the drivers to operate in order to establish communication with the Nexus.
Finally, you need also the latest Java packages including development SDK's, which you'll be asked to install during the Google package installation.
If all of this hasn't put you off then you're ready to root and flash.
One last thought on the subject - the Nexus range is definately the easiest of any phones I have come across to unlock and root and generally play around with. Read, read and read up on the subject.