There is no universal method to doing this, the fact is that everyone is different in the reason for why they believe what they believe and what it is that will change they’re mind. This is what I reccomend
Step 1.
Decide whether or not this person can actually be convinced of your position or of any position that is not theirs. Sometimes it’s just better to come out and ask “what would convince you of my point?”. They cannot answer that nothing can because that makes them look like a close minded fool. Based upon their criteria (assuming you believe them and there aren’t other ) If the answer is that they cannot then there are other reasons for debating them, but the question of how to convince them has been answered: You cannot.
Step 2.
Attempt to fill the requirements that they set out. Continually refer to THEIR values. You are trying to convince them. As the praxeological law states men act according to their value preferences and therefore you must appeal to what it is that they want and they believe in. Remember that a belief should be a means, not an ends. You are a socialist, not because you value socialism, but because you value the ideals and the state of affairs brought about by socialism. If this can be met in a libertarian society then you should become a libertarian.
Step 3.
Be reasonable and to the point. Always try to give them some sort of exit strategy that prevents them from being humiliated. Assuming that the point of the debate is to convince them then you have to accept the fact that you are likely not going to be able to get them to go all the way. Especially when the debate is confrontational it’s extremely difficult to admitt that you were wrong to another person face to face. Allow them to take a moderate few and sow the seeds of libertarianism and doubt. Trying to make sure that it’s over time is a good idea too, of course. This also means that you must be sure to remain civil so as not to make it more confrontational and a matter of person vs. person, the loser being an idiot, instead we have to ensure that it’s ideas vs. ideas and that it’s understandable to believe what they believe, it’s a small mistake that needs to be corrected. Another very important thing to do is to ensure that you do not get sidetracked. I’ve done this so many times that it’s ridiculous, keep to the issue don’t get into arguments over irrelevant side conversations. Connect everything over to the actual issue at hand, make it understandable and clear.
Step 4.
Realize when a debate is not going anywhere and simply attempt to back out as well as possible.
Step 5.
Remember, you’re a salesman, you’re trying to sell an idea, keep everything that you can in mind, don’t talk about something that’s going to take ages to explain, keep it simple and keep it appealing.
Step 6.
Know the basic statist fallacies. Be able to argue against democracy, market misconceptions, the larger historical misconceptions, anarchistic misconceptions , incentive misconceptions, and basic logical fallacies such as is/ought, ad hominemm and most importantly correlation/causation.
Step 7.
Don’t get too wrapped up in it, remember, it’s just one person, you’re just one person. Don’t be too uptight, be fun while you’re talking, make it a fun conversation and don’t make them feel like they need to be angry about the issue. It’s all cool.
Also, pick out your targets selectively and attempt to research topics that you know are going to be important to them, don’t spend your time even trying to strike up conversations with someone who is unlikely to respond well. There’s a reason why democracy doesn’t work as a universal system.
Step 8. Send them to talk to Neodoxy, or give them links to his (upcoming) videos!!! 
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