If you do not have Samsung’s KIES 2.0 installed, download and install it. Correct USB drivers must be installed, so that programs can communicate with the device. Reboot computer after KIES installation.
Make sure that your phone is in USB debugging mode (Settings -> Applications -> Development -> USB debugging)
Reboot your phone into download mode (Turn the phone off, then power it on again by pressing and holding VolumeDown + Home + Power simultaneously)
Once the phone reboots (still plugged in) start SuperOneClick
Reboot the phone
Congrats you have a rooted Samsung Galaxy S2!
While this is a nearly flawless device without having to root it of course we all like the total control and freedom of no restraints. As always this is completely educational and you take all risks associated with following these instructions. We like to help you get root access on your phone but don’t need you knocking down our door if you get bricked somehow.