I am a student trying to understand how this is possible. I've done some research on the web with not many sources showing up with solutions to this problem that are usable. What techniques are used to give an approximation of an FIR filter using IIR filters with say the same order?
Sure there is.
The simplest version would be to calculate the transfer function of your FIR filter, sample it on some meaningful frequency grid and then shove it into
invfreqz() to design the IIR filter.
Depening on you FIR filter this may work well or be a total disaster. In my experience invfreqz() does often very poorly.
If that's not good enough you can certainly write your own search an optimization algorithm. However, this is NOT a beginner project and requires significant math and coding skills.