2) Install the drivers for your computer (XP/Vista/win7)
3) Download, unzip and install the SuperOneClickRoot 1.7 HERE
4) Run the SuperOneClickRoot program after enabling USB debugging mode on your Samsung Mesmerize which is plugged into your USB port.
5) Your Mesmerize is rooted now.
DISCLAIMER: CLShortFuse and RootzWiki are not liable or responsible for any damages to your phones, this is solely the users decision to "root" their phone. Enjoy!
This method will no longer work for Gingerbread.
There is no other method to root than to push su binary, sqlite3 and busybox to system/bin via adb as well as superuser.apk to system/app. Make sure su permissions are set to 06755.