Step One
Press to launch Safari from your Springboard.
Step Two
Press to select the address bar and input http://jailbreakme.com then press the Done button.
Step Three
To begin the jailbreak simply move the slider to right.
Step Four
You will be displayed a status bar as the download progresses.
Step Five
Once the download is complete the jailbreak process will begin
Step Six
Once you are notified that the jailbreak process is complete press the OK button.
Press the Home button to reveal Cydia on your desktop!

Once this done, you can also unlock your iPhone (follow relevant blog).