*NOTE: please do not comment asking questions about other devices or software. This is the guide I edited/used and has worked for me.
It was hard for me to find a good list of instructions to Jailbreak my iPhone. After a lot of research and skepticism, I found a guide that worked. This guide worked for me, and I cannot guarantee it will work for you. Jailbreaking is Legal. Refer to the iOS jailbreaking wiki page for more information.
My Phone Information
Model: Apple iPhone 4S
Firmware Version: 5.1.1 (9B206) [Found @ Settings > General > About]
Link to a YouTube video of an example of Jailbreaking 5.1.1 with redsn0w: Jailbreak 5.1.1 Untethered
Link to downloading redsn0w: Download (iPhone Dev Website)
Directions:
1. Download Download redsn0w 0.9.14b2 (Windows) using the link above.
2. Use iTunes to Sync your iPhone 4s
3. Use iTunes to Backup your iPhone 4s with right click, back up (do this if you back up to the cloud).
4. Erase your iphone: Settings > General > Reset > Erase All content and settings
5. When erase is complete, set up your iPhone as a New Phone and activate (you will need wifi, apple ID and pw)
5. Ensure your running iOS 5.1.1 (Settings
6. Open redsn0w and click Jailbreak.
7. Follow instructions and allow your iPhone to reboot itself.
8. Wait about a minute or two after reboot and you will see Cydia is available.
9. Open Cydia (it will say Preparing Filesystem for a minute). When this finishes, you Jailbreak is complete.
10. To restore your old settings, open iTunes, find your phone, choose the restore date and click continue.
Your Jailbreak is now complete. Download apps through the appstore or Cydia.
My Useful Cydia Information: Sources / Applications