Depending on the target, you'd either have some talking points to "debate" (sometimes with yourself/other anons working alongside you) or you'd go in there guns blazing trying to cause as much damage/chaos as you can. However, even then you can't go out there yelling slurs (you'd just get banned instantly); you have to maintain some level of plausible deniability by framing things as "jokes" or thought experiments.
You purposely do bad-faith arguments because the time it takes for them to dig up sources and refute you is longer than it takes for you to make stuff up. You can vary how obvious the bad faith argument is; when you want to troll you make very stupid claims (I once claimed I was a graduate of "Harvad University" and when people assumed that I meant "Harvard" I would correct them right down to Photoshopped images).
When you just want to cause dissent you do exactly what those /pol/ screenshots do: you get to a thread early (sometimes you even make it yourself) and present reasonable-sounding arguments which are completely false if anyone bothers to look into them. If someone does, you bury the message under strawmen, downvotes, reports, and sockpuppets.