If your device has firmware of 4.0.1 or below, it is very easy to jailbreak, and you don't even need a computer. Simply open safari on your device and go to the website "www.jailbreakme.com" and follow the onscreen instructions.
If your device is at firmware 4.1, it can also be jailbroken using Limera1n on mac osx or windows operating systems on your computer. Instructions can be found here
If your device is at firmware 4.2.1, the only jailbreak you can perform is tethered and you will need to connect your device to a computer whenever you wish to turn it on. I do not recommend jailbreaking your device in this instance and would instead advise you to wait for an alternative jailbreaking method.
If you have any interest in jailbreaking your device in the future, I would advise you not to update your iPhone firmware at any time until you know that the firmware you are updating to can be jailbroken. Remember also that if you update the firmware on a jailbroken phone your jailbreak will be lost.
