AO3 filters are incredible. The show ended over a decade ago but you're only getting around to watching it now, and you want to avoid spoilers for later seasons? No worries; you can filter out anything posted/updated after a given air date. Don't want to see crossovers? Guess what -- you don't have to. Three clicks is all it takes to make them go away. ONLY want crossovers? They've got that option, too. In a hurry and only have a few minutes to read? Filter out everything over whatever word count you consider to be "too long." Absolutely can't stand this one character/trope/relationship? Exclude, exclude, exclude. And all they ask in return is that you tag your stuff properly. Incredible.
If you haven't seen the filters before, you might be finding fics via searching. Search is great (and you can get *really* specific with it), but it doesn't have the quick filter menu.
Tap on a tag you're interested in reading (just at the top of a fic, for example). That will bring you to a results page that shows every fic that uses that tag. To get rid of the ones you don't want, look right above the works list to the buttons and tap on Filters. (if you're on a computer, the filters will already be there, on the right hand side of your screen).
Once you've found the filter menu, it's like the OP said. There are a *lot* of options for you to choose from. You can tap on any of them to open up a sub menu with specifics.
For relationship/character/trope tags, AO3 will automatically show you the top ten most-tagged ones within the tag you're already looking at. If the one you want to exclude isn't in that list, you can type it into the "Other tags to exclude" box and AO3 will give you a dropdown to pick from. You can add a theoretically unlimited number of tags to your exclude list, but I think it's possible to have a list that breaks things eventually. I've never personally hit it? But I bet someone out there has.
You can also Include things you want to guarantee are tagged, but be careful with that filter. Include filters stack on top of each other, so if you Include 3 different tags, you'll only get fics that have all three of them tagged. You won't get ones that have*any* of them tagged. For more info on how to do an "any of these tags" filter, see this post over here.