Introduced by the iPhone dev team, the new jailbreak - called Official 1.1.3 Upgrader - works by cracking Apple's application-signing method, which (unfortunately) may have negative consequences when it comes time to install official, Apple approved software. Rather than a PC or Mac, all that's required to set this jailbreak upgrade in motion is Wi-Fi connection and an outlet, the latter to make sure your iPhone/iPod touchs power source doesn't poop out in the middle of installation.
For directions how to install this jailbreak, see here. Remember, the new computer-less 1.1.3 jailbreak method is only for those who've already jailbroken their 1.1.2 iPhone/iPod touch. If you haven't jailbroken 1.1.3 yet - or if simply require more detailed directions - head over here. We recommend you check out the info at the previous link first, however.
As we've mentioned before, performing any type of unofficial software upgrade, especially a jailbreak, isn't for the faint of heart. Jailbreaks, in particular, have been known to cause trouble for some iPhon/iPod touch users. They do open up a whole new world of applications to the user, though. So the risk, for many, is worth the potential benefit.