Below are the following instructions on how to jailbreak your iPhone and iPod touch using BlackRa1n for Mac.
Attention to new iPod touch or newer iPhone 3GS, BlackRa1n only supports a tethered jailbreak. This means that once jailbroken you should not let your battery die. If it does die you will need to reconnect it to the computer and use BlackRa1n to boot it.
Open your web browser of choice and navigate to http://www.blackra1n.com. Click the Apple logo at the bottom of the screen.
When prompted save the download to your desktop
Then double click the downloaded blackra1n zip file to extract the application, then double click the application icon to launch the program.
Make sure your iPhone or iPod is connected to the computer then click the large make it ra1n button.
You will see a picture of GeoHot that replaces the regular recovery mode screen on your device. blackra1n will run and then your device will reboot.
Once your device reboots it will be jailbroken and you will notice a blackra1n icon on the desktop.
Make sure you have an internet connection and press to launch the application.
Choose the installer application of your choice then press the Install button at the top right of the screen BlackRa1n will begin to download and install the package you selected.
Once complete BlackRa1n will respring your iPhone and you will find the installer package of your choice on the Springboard.