This method supports the following iDevices:
• iPod Touch 1G on iOS 3.1.2
• iPod Touch 1G on iOS 3.1.3
• iPod Touch 2G on iOS 3.1.2
• iPod Touch 2G on iOS 3.1.3
• iPod Touch 2G on iOS 4.0
• iPod Touch 3G on iOS 3.1.2
• iPod Touch 3G on iOS 3.1.3
• iPod Touch 3G on iOS 4.0
• iPad on iOS 3.2
• iPad on iOS 3.2.1
• iPhone 3G on iOS 3.1.2
• iPhone 3G on iOS 3.1.3
• iPhone 3G on iOS 4.0
• iPhone 3G on iOS 4.0.1
• iPhone 3G[S] iOS on 3.1.2
• iPhone 3G[S] iOS on 3.1.3
• iPhone 3G[S] iOS on 4.0
• iPhone 3G[S] iOS on 4.0.1
• iPhone 4 on iOS 4.0
• iPhone 4 on iOS 4.0.1

The first thing you should do before jailbreaking is backup your iDevice with iTunes in case something goes wrong.

The current method for jailbreaking mostly all iDevices is a PDF exploit within the Mobile Safari application. Because of this, you do not need a computer to jailbreak, everything is done right from the device itself using the application.

After you have a successful backup launch your Mobile Safari app and go to the url http://jailbreakme.com When you get there it will look like this:

Slide the bar at the bottom just as if you were going to unlock your phone:

The download will initiate after you slide, I usually do it on a wifi connection if I can because it seems to go faster. After it downloads it will take a minute or two to install and then you will see this screen:

At this time you can close out of Mobile Safari and when you get to your springboard you should now see a Cydia application indicating that you have jailbroken your device successfully! Please note that you will now see a string of pixels on the boot screen when you restart your phone. This is completely normal.