Traditionally for better or for worse, undergraduate representation comes by way of a student council, with a single person elected to a chair on the larger university advisory council (the structure can be different depending on the university, I'm generalizing).
https://mitgsu.org/updates/we-have-an-election-date-vote-yes...
Note that for instance if you're there with a fellowship and aren't getting a partial RA/TA assignment as well then you're not eligible. I know that some masters students pay for their tuition, so they might not be eligible either since they're not getting a stipend.
https://www.inf.elte.hu/en/content/doctoral-training.t.1616?...
[0] I expect that if someone wants to do a PhD in teaching methodology they might have to still do some teaching