The very first step is to know the fallacies. Find a list.
The second step is to familiarise yourself with them. Learn the fallacies. It can also be called sophism in some languages. Familiarising yourself with them will allow you to recognise them.
Third is to be vigilant during a conversation to detect them. Sometimes you will be the one to use them.
The easiest, and amont the most common, are fallacies tied to reputation: when you consider something right or wrong because of who made the statement. It’s sketchy because it can be used as a shortcut in conversation, but by itself the truth or wrongness of the argument doesn’t depend on who said it, never. But some people have demonstrated expertise or they habit of lying or manipulating. Other fallacies usually involve the language or the logic, so it’s harder to detect, but it’s a great mental exercise.