Don't just watch the show. Look at the archived threads on /co/ during the show's airing, look at the Reddit threads too, if you want.
Look at fan art, read fanfic (I recommend The Star Butterfly Effect by Xirema on AO3). Try making your own fan works. Try to see the spark that made a fandom, see what made about the show made people tick.
Make it so that you're a viewer at the time the show was still airing. It's an interesting thing to immerse yourself in a time capsule of a fandom. Recently I've been going through Gravity Falls threads from back when it was airing, and it's an interesting thing to observe as an outsider, trying to simulate what it's like to be in it. It's like sub-cultural archaeology.