Start by backing up all the data on iTunes. Depending on the specific model of your phone, you can now download a jailbreak tool from http://www.jailbreaktools.com/. Follow the on-screen steps to complete the jailbreak.
You should back it up to iTunes or iCloud (I recommend iCloud) although there is only a small chance that you're settings will be erased) and download the jail breaking software. iOS 6.1.3 jail breaking does not exist yet but all others do. I recommend evasi0n jailbreaking. Download it on you're computer and then follow the instructions on the software.
Some things you should be aware of before jailbreaking: