I have jailbroken and unlocked my phone myself before without using jailbreakme.com. It is difficult but very possible, however, I don't think you will get anyone to explain to you exactly how to do it simply because it's hard and many steps. I can give you some vague information that will help and some advice. Just to note I'm not great with computers and I now know a guy who does everything for me for 20 bucks. If you can find someone like that it's way worth it.
Do NOT upgrade your phone through iTunes. It will not only unjailbreak your phone but will load the latest iOS onto it which would be tethered jailbreak and very difficult to do. You will have to search for a newer firmware and download that to your computer. Through a series of steps you can update your phone with that new firmware. I recommend just getting iOS firmware 4.1. It runs far smoother than any newer firmwares.
I disagree with the fellow that said you need a new phone and the newest firmware. There are some things you may not be able to run and apps that require newer firmware, but you probably won't even notice it. Also, the jailbreak, in my opinion, is far more valuable and important than the few apps that won't run on 4.1. In fact, you may even be able to find the same app that can work on your firmware through xxxxxxxxxx or cydia.
Anyway, in order for you to learn how to upgrade your firmware and rejailbreaking or keeping the jailbreak, I recommend doing some research and find a good YouTube video that has good rating and comments on it working. A reliable website that gives a step by step guide would work too. If you start researching, you will find it.
Good luck! ^_^
