A conditional statement is any statement in the "If..., then..." form. The converse switches the hypothesis and the conclusion. It's easiest to demonstrate this in an example:
Our statement will be "If an animal is a dog, then it has four legs." Now to switch the hypothesis and conclusion, we take the "an animal is a dog" part, and switch it with the "it has four legs" part". I will change the wording slightly so the sentence still makes grammatical sense: "If an animal has four legs, then it is a dog".
Now the final statement from the previous example serves as the perfect false conditional statement with a true converse:
Statement: "If an animal has four legs, then it is a dog", clearly false.
Converse: "If an animal is a dog, then it has four legs", a true statement.
