There are at least several if not many models of the S4 mini. Some of these are SGH-I217, I9195, SPH-L520, SGH-I257, etc. They do not necessarily all use the exactly same root procedure. So you do have to do a thorough search, perhaps thru other S4 mini forums in addition to this one [i read 5 each day altho this one is the most technical]. With each procedure you will find the warning that it may not work with your phone and that you assume all the risk. I have not yet seen a procedure that was described at a beginner level. Each procedure is complicated and technical and assumes that you know all the jargon etc.
So be prepared to spend some time, perhaps a few weeks or more, thoroughly researching the procedure for your specific model.