It has been a while since we have been waiting for an untethered Jailbreak for iOS 5.1 but it’s been done. Go ahead and download Absinthe 2.0 to allow installation of Cydia to your iPhone 4S or iPhone 4. Make sure you use TinyUmbrella to backup you SHSH blobs in case of disaster.
Jailbreaking your device is as easy as plugging it in and running Absinthe 2.0 and hitting the Jailbreak button. It took about six minutes for my iPhone 4S to complete the process as well as a reboot but it progressed pretty smoothly. As always, do this on your own risk and backup your iPhone through iTunes or iCloud before progressing.