The Absinthe tools are really easy to use - jailbreaking has gotten much easier than it used to be. However, the dev teams are hard at work on getting their tools to work with the latest iOS version/chip version combinations so it's hit or miss with if you will actually be able to do it.
Absinthe is currently only compatible with 5.0.1 and 5.1.1 (you can see greenpois0n.com for a bit of info).
One thing to look out for is that it can be confusing but being that you have a 4S that narrows it down a bit - you will probably need to wait until they update Absinthe to jailbreak, unless you are fortunate enough to not have updated the firmware yet.
On the subject of unlocking, that's a different story - in case you're not sure of the difference, unlocking means being able to use different carrier SIM cards where as jailbreaking means being able to use non approved apps (it's a common mistake, so that's why I mention it here).
Unlocking can be done a few different ways (in the US, I'm unsure exactly the process in other countries). In the US, Sprint WorldWide customer service will unlock your phone if your account has been in good standing for 90 days (I've had 5 iPhones unlocked this way) and as long as there are no other holds on your account. AT&T will unlock a 4S that isn't on contract (I'm unsure if it has to be an AT&T phone originally) and I think Verizon Wireless has a similar policy (but I don't know for certain).
One thing you will want to watch out for are street vendors that say they can unlock your iPhone - they can't, don't waste your money.
iClarified actually has a pretty good walkthrough wizard for both unlocking and jailbreaking here:
Hope that helps.