Ensure your iPhone is on iOS 6.0 to iOS 6.1 then perform a backup of your iPhone.
Create a folder called Pwnage on your desktop and download the Evasi0n utility into the folder. You can find download links for Evasi0n here.
Double click the Evasi0n dmg file from the Pwnage folder on your desktop to mount it.
Drag the Evasi0n application from the mounted dmg into the Pwnage folder on your desktop.
Right click (or Control+Click) the Evasi0n app icon then select Open from the contextual menu to launch the application. If prompted to confirm, click the Open button again.
Ensure your iPhone is connected to the computer via a USB cable if you haven't already.
Remove any lock screen passcodes on your device then click the Jailbreak button to begin.
The app will retrieve information from the device to generate jailbreak data, inject stage 1 jailbreak data, reboot the device, wait for the device to be ready, inject stage 2 jailbreak data, upload Cydia, and upload the Cydia packages list.
You will then be asked to unlock your device and tap the new 'Jailbreak' app icon. It is imperative that you only tap the icon once. The app will open and immediately close.
Evasi0n will then inject the remount payload, remount the root filesystem, prepare the final jailbreak data, inject the final jailbreak data, and complete!
Your iPhone will now reboot with Cydia on the SpringBoard!