Hello Mstadt and welcome!
Do you know what generation Mac Mini you have? I am almost certain that all Mac Minis, regardless of generation, have Mic inputs. If you look at the attached picture, look above the USB ports, you should see an headphone jack and an audio input jack. A Mic can be plugged into the Audio input jack. I hope this helps you and I hope you have some sort of Audio input jack on your computer.
NOTE: The symbol for the jack is not a little microphone, it's a little hour glass like thing with a bubble in the center of it.
Also, if your computer does not have that input, you can always get yourself a USB Microphone. They tend to sound and work better. That's an alternative solution for you. Again, I hope this helps you and please let us know if you need further assistance.
Cheerio
Searay