I finally got around jail breaking my iPhone 4s, and it was easy enough. Here are the steps I used:

Computer OS: MacOS Lion 10.7.2

Connected phone to computer using the USB cable.

Opened up iTunes

Right mouse clicked on my phone in iTunes, and selected Backup

Download the Absinthe program from http://cache.greenpois0n.com/dl/absinthe-mac-0.1.2-2.zip.

Unzipped the program by double clicking it.

I closed iTunes, and launched Absinthe.

Clicked “Jailbreak”. This step take quite and while, and looks like it is restoring.

Once complete, you will see a message stating that you are almost done.

Unlock you phone, and tap the Absinthe icon that was added.

This will briefly display the Greenp0ison website, and then reboot.

This will replace the Absinthe icon with a Cydia icon.

Launch Cydia, and you get a “Preparing Filesystem” message and the Springboard will re-launch.

Update: I had to re-setup the Wi-Fi Sync. I did this by plugging my phone into my computer with iTunes running. I turned off Wi-Fi Sync by unchecking it in iTunes, and applying. Then, I turned it back on and applied. This took care of it.