I just give you a hint of what you need, there are lots of guides on this forum just search for them and read carefully
First of all you must know that installing custom ROMs is potentially dangerous, it may brick your phone and it voids your warranty, you do it at your own risk.
Make sure your phone is supported by the software you're going to install, S3 mini aren't all equal, check for model number.
Before installing CM 11 you should install a custom recovery (TWRP from maclaw.pl is recommended for installing kitkat), than you can do a nandroid backup and restore it if something goes wrong, and install custom ROMs very easily.
To flash the custom recovery you need odin in windows (you can find it on maclaw.pl download page) or heimdall in linux. About odin there are lots of tutorials, just search for them, but if you need help with heimdall just ask for it