Am I supposed to resign?


Nearly 100% of professional games end in resignation.
Nearly 100% of beginner games don't.
As you get better, resignation will be more common. Sometimes not resigning is seen as rude, but never resign because you feel like you have to. Resign because you think the position is a trivially easy win for your opponent, and you can't learn anything by watching them do it.
If there's any reason to think they might mess up (running out of time, a complicated position, you have a few tricks left, their rating is really low, they've made a lot of mistakes that game, etc) then keep playing.
Telestu: a much more diplomatic way to phrase it is:
No, because if I resign I won't get to see your winning Technique.

Telestu: a much more diplomatic way to phrase it is:
No, because if I resign I won't get to see your winning Technique.
That's a good way to say it.
I've certainly done that before. After being outplayed the whole game, and I know my opponent is a better player than me, and I know I'm losing, but I don't quite see why my position isn't a bit of an annoying fortress... so I keep playing moves to see how they dismantle me. After the win looks trivial, I resign.