Whatever you do, DO NOT UPDATE TO 1.1.3 VIA ITUNES!!!!!!!!!
Doing so can result in the loss of phone functions.
The guide on this site is probably the best and most comprehensive at the moment.
I would advise that if you are not sure the dont do it.
If you do take the plunge please read the guide over many times until you feel that you know it inside out, if you miss even the smallest step it will go wrong for you.
If you already have a jailbroken 1.1.1 iphone then start at the point in the guide that says 'start here if you have a jailbroken 1.1.1 iphone.'
Can i ask exactly why you wanna upgrade anyway, there is not much on 1.1.3 of much use. Plus with all of the reported problems both with jailbroken iphones and offical 1.1.3 firmwares, you could do more damage than good.