You need iTunes to run this jailbreak, but you cannot use the latest version. Download a past version or the jailbreak tool won't be able to detect your device. Here's how to do it:
1. Turn off passcode and find my iphone in settings.
2. Plug in your iPhone to your Windows PC. The 8.1.3 jailbreak doesn't support Macs. It hopefully will in the near future, but not yet. If you have a Mac you can run Parallels or another software to run Windows operations.
3. Go to this link:
http://www.taig.com/
4. Download the 8.1.3-8.3 jailbreak tool (big blue button)
5. Open Jailbreak tool and hit "Start." I recommend un-checking 3K Assistant (It's an application that allows you to get free games and apps, however there are better alternatives like AppCake and vShare.
6. Wait for the jailbreak to complete. Don't use your iPhone during this time.
And you're done. Cydia will be on your page of apps furthest to the right. Enjoy!