How to Argue Using the Socratic Method
To argue using the Socratic method, start by asking questions to make sure you understand what the other person is claiming, then ask for evidence to support their claims. Next, challenge their assumptions by focusing on the ideas that aren't supported by evidence. You can also find exceptions, like a set of circumstances in which the person's statement would be false. Once you uncover the gaps in the person's argument, ask them to reformulate their claim to account for the exceptions and unsupported claims.
Sum up the person’s argument. Identify what the other person is arguing. For example, someone might say, “It's best to give money away instead of spending it.” Often, people will believe that they are espousing common sense, which no one would disagree with. If you don't understand what someone is arguing, ask them to clarify their beliefs. You can ask, “I don't understand. What are you trying to say?” or “Could you restate that?” Ask for evidence. Before beginning to really challenge a person's point of view, you should ask them about their evidence. A person might quickly realize that they are merely repeating something they have heard before without thinking critically. You can ask the following questions to uncover evidence: “Why do you believe that is true?” “Please explain your reasoning.” “What has lead you to that belief?” Challenge their assumptions. Ideas are like building blocks. Your conclusion rests on other blocks, some of which might be unproven. When an idea is unproven, it is an assumption—and assumptions can sometimes be wrong. After asking a person for their evidence, zero in on the ideas which aren't supported by evidence. These are their assumptions. For example, someone might say you should give away money because having too much money makes you greedy. This person is assuming someone doesn't spend all of their available money on necessities. You can say, “But are you assuming people have money to give away after buying necessities? Is it best for these people to give their money away?” Find an exception. Identify a set of circumstances where the person's statement would be false. For example, is it always good to give away your money? You can think of many situations where a selfless person might cause more harm than good. Consider the following: The person who wants your money is a drug addict. Ask your opponent, “Should I give my money away to someone who wants to buy drugs?” If the person says no, then follow up and ask why, which will help you tease out the other person's thinking. You must provide food and shelter. Formulate this as a question: “Should I give away all my money when my elderly mum is dependent on me?” Ask the other person to reformulate their argument. Once they concede that the exception exists, they should reformulate their argument to account for the exception. For example, they might say, “People should give their money away if doing so would benefit society.” Continue to ask questions or raise exceptions. In the example above, you can ask the person to define what “benefits society.” You can also ask questions to pin them down if they are confused. You should continue this process until you can't invalidate the statement any more. Avoid getting nasty. The Socratic method is not about proving people wrong, so don't be aggressive in with your questions. If your goal is to win an argument, then you should seek out different Greek philosophers, such as the Sophists. Indeed, the key to the Socratic method is to be humble. Don't assume that anyone knows anything for sure. Question every premise. If the other person starts to get flustered, you can say, “I'm just playing Devil's Advocate” or “I'm trying to understand all sides of your thinking.” You might enjoy the other person's confusion a little too much. Try not to gloat. Remind yourself that Socrates didn't have answers for every question he asked, which is typical of an exchange using the Socratic method. Prepare for class. In law school, a professor might call on you at random to discuss a case. There is no way to anticipate the questions your professor will ask. However, you can put yourself in the best position by thoroughly reading your assigned material and briefing cases. Remain calm. You might feel panic when called on. However, if you've done your reading, then you've put yourself in the best position to engage in a Socratic exchange. Take a deep breath and then smile. It's best to think of the Socratic questioning as a dialogue between you and your professor. Block out the other students listening in. Answer questions honestly. The purpose of the Socratic method is to identify the contradictions and limitations in our own knowledge. For this reason, you need to be honest in your answers. Don't try to anticipate what you think the professor wants to hear. If you're in law school, you should know the facts of the case and the court's holding. However, apart from the facts, there are rarely “right” or “wrong” answers. Try to get into the spirit of the questioning by understanding its purpose: not to find the right answer, but to understand what you truly think. Be as clear as possible. You'll handle some complicated material in class, so your answers to questions might not be “yes” or “no.” Try to answer as clearly and completely as possible so that your professor understands your point. At the same time, strive to be as brief as possible. There's no reason to give a long-winded answer if one isn't required. Realize no one is judging you. As you listen to a Socratic exchange, you are probably answering the questions yourself and struggling along with your classmate. Accordingly, there is no reason to be embarrassed if you are on the receiving end of Socratic questioning and have a deer-in-the-headlights look. Admit when you are stumped. You might reach a point where you can't resolve the contradictions in your thinking. At this point you are truly stumped. Feel free to admit that you don't know how to answer a question. Remember that the Socratic method is something you can use with yourself throughout your life. You should constantly interrogate what you think is true. 
Sum up the person’s argument. Ask for evidence. Challenge their assumptions. Find an exception. Ask the other person to reformulate their argument. Continue to ask questions or raise exceptions. Avoid getting nasty. Prepare for class. Remain calm. Answer questions honestly. Be as clear as possible. Realize no one is judging you. Admit when you are stumped. 