For most people out there they'll just google how to jailbreak however there are pros and cons to each method some, most perhaps, are just minor but can make a difference in what you are looking for.
This is perhaps one of the most known methods to jailbreak an iPod, or iPhone. For those that might need to jailbreak while on the go, and no access to internet this is probably not the best method, as in order to get to the steps where the jailbreak gets installed, your pc/mac needs to download some info first. What is nice about this jailbreak, from the firmwares that I've jailbroken is it allows for direct access to the file system as soon as the device is jailbroken, allowing you to setup the cydia auto install folders and whatever else you may want to do. Other firmwares require you to first install through cydia, afc2add, which allows a pc/mac to access the filesystem. This may be a benifit to some, it may not, for me it was as I lived in an area where I didn't have access to wireless, thus I had to download through Cyder, a program for pc that allows download from cydia repos, all my apps and install through auto install. This method of installing isn't for the not to tech savy as it requires some knowledge of dependencies and other things. In my opinion I find redsnow to be a great jailbreak method.
Spirit on the other hand is great for those that do on the go jailbreaking for friends and what not, it currently only jailbreaks 3.x firmware for iPhone, iPad, and iPod Touch. It is very simple to use, probably one of the easiest methods to use. Theres not much explaining need here it will get you to the same point as redsnow, more or less.
I haven't had much experience with this method, however for more info on the new release go to this link.