Hope your holiday vacation has been good.
I see 3 main reasons why you would want to root your Android phone…
1. You have a lot of preinstalled crapware/bloatware on your phone and can’t delete it unless you are rooted.
2. You want to use 4G tethering on your phone but your carrier charges you extra for doing so. Rooting could bypass this and let you tether for free.
3. There are cool Android apps in the Google Play store that you want to use. But they only work on rooted phones.
I am sure I missed a few, but the top 3 are my main reason I have wanted to root any phone I have owned.
If none of the 3 options I have listed interest you, it is not worth rooting your phone.
I have rooted 3 phones in the past. I found the best phone-specific rooting guides at the xda forums. Here is a how-to rooting thread within a special forum dedicated to several Galaxy S4 models, including the AT&T version.
The first 2 posters within that thread list different instructions. See which method is easier for you.
Disclaimer: There is a small chance you will brick your phone (it will be useless) while rooting. Also if there is an AT&T S4 update you will not be able to download it when it is rooted, you must unroot your phone to install AT&T S4 updates. Last, this does not matter on your S4 since it is older, but rooting cancels phone manufacturer warranties.