Hopefully you never find yourself in a situation where you have to engage with someone who believes in a flat Earth. On the off chance that you do, don't go in unprepared! Here's some hard ammunition you can use to thoroughly debunk them.
Meteorologist Keith Carson provides a number of arguments you can use if you ever find yourself going toe-to-toe with a flat-Earther.
The most obvious is "all the pictures we have of an oblique spheroid Earth" and if that's not enough, there's always the live feed from the International Space Station.
If that doesn't do it, you can tackle some of their explanations head on, such as how the sun and moon work. If they state the sun is a spotlight, which circles above the Earth in concert with the moon, Carson has you covered:
You would never see the moon during that day, daylight hours would never change and most importantly, you would always see the sun, even during the night.
For that last point, Carson uses the example of spotlights at a gig -- even when they're not directly on you, you can still see them clearly in the dark.
Of course, even when faced with facts, you still might not be able to convince them. At the very least, you'll make them look especially idiotic to everyone else involved in the conversation.