I was going to use screenshots as a guide, but its so easy to do that I’m not even going to bother. Heres how to do it:
1. Go to http://blackra1n.com/ and click either the Windows logo if you’re using Windows or the Apple logo if you’re on a mac.
2. Run the application after it downloads.
3. Click “make it rain”
It will show the picture you saw on that website on the device’s screen for a bit, and after it reboots it should be jailbroken. It will have installed an app called blackra1n, open it and install whatever installer you want, and enjoy your jailbroken iPhone or iPod touch. I’m pretty sure this works for each generation of both devices.