If it’s the “people” kind then what you have to realize is actual conspiracies happen all the time - there are many interwoven plots, ulterior motives, and hidden agendas going on all around you.
People are generally good at noticing that something doesn’t add up - much worse at working out what might have actually happened.
They have also been lied to and mislead by our institutions often enough that they are unlikely to trust your sources or corrections.
The only long term solution I can think of is to clean up our institutions - but that won’t happen overnight.
If it’s the “flat earth” kind - overall these people are higher than average intelligence and fairly well versed in the topics they are discussing - and so unless you yourself understand the subject matter they will run circles around you.
This second group are actually really interesting to talk to and ask interesting questions - for example why do pilots fly without adjusting for the curvature of the earth? Why do many long distance snipers not adjust for the curvature of the earth? Etc etc.
I’m sure there are great scientific explanations - and I’m also sure that many in the flat earth crowd would listen.