Persuasive writing begins with being able to communicate with your reader in a language they can understand.  This does not mean that you need to dumb down your language or show off how much you know.  Both can be equally frustrating if the person that you are talking to does not understand what you are trying to say.   Write in a language that sounds natural and unaffected.  Be clear and concise when presenting your subject.  Make your points using concrete details that your audience can relate to. If you follow this simple advice, you’ll see much better results from your web, print, and email copywriting.

Some of the best teachers that I ever had were able to take abstract ideas and put them in a language that everyone could understand.  They were masters of keeping their audience engaged by finding ways of making their subject relevant in order to reach as many people as possible.  They could do this because their mastery of the material allowed them to present it in any way they needed to in order to reach their audience.   If you asked them a question and they spoke to you individually you knew that they knew their stuff because they could explain it in a way that you could understand.
I found one such teacher when I took Calculus in college.  I actually found Calculus to be one of the most enjoyable classes I took and it was not because I was a math person.  Every subject uses its own particular vocabulary and can seem complicated unless you are able to keep up.  This is especially true when you use that same vocabulary to build upon further concepts.  My calculus teacher had us solve equations based on word problems that had to do with episodes of the X-Files, a popular TV show at the time.   This made class more interesting and I began understanding new concepts effortlessly because equations involved diabolical schemes from the Smoking Man.
In order to write persuasively you must first master the material you are presenting and be able to explain it in as many ways as possible. That way you can reach as many people in your audience as possible.  Like a good teacher you must master the art of communication.   If given the opportunity you should be confident enough to present your material to every individual member of your audience in a way that each and every one of them is able to get.  When you are able to do this you establish your credibility.
You must empathize with the person you are writing for.   Empathy allows you to see things from another person’s point of view because you are able to feel what they feel.  In order to effectively persuade you must be able to view things the way the people you are communicating with view them. You are going to need to make a practice of empathy in your daily lives as this is the only way of truly understanding the different ways in which diverse sets of people think and feel.  In order to master persuasion you must learn to feel what other people feel when you attempt to communicate with them.
When you empathize with your audience you are not just connecting with them but they are also connecting with you.  Empathy bridges divides.  In order to speak in a language that another person understands we must know what it feels like to think and feel the way they do. When you do this they are more receptive to the way you think and feel.   If you empathize with others they are more likely to empathize with you.  This makes them more persuadable because they are more willing to place themselves in your shoes in order to understand how you think and feel.
If you can then follow this with reasoned arguments then they will consider your reasons and place themselves in your worldview.  Some people may be initially surprised or confused by your empathy at first.  They may initially mistrust your attempts to empathize with them and think you are simply trying to be manipulative.  However,  once you establish that you feel the way they feel through sustained effort in your communication with them then this quickly leads to trust.  In order to master persuasion you must be able to establish trust with your audience.
For some it will be harder to come around toward your worldview than others.   You are going to want to pay special attention to people that do not see the world the way you do.   Remember,  a good teacher is able to take questions from anyone in the room and present learning in a way that everyone understands.  They have a mastery of their material and this allows them to present it in more than one way.
You will have people that understand what you are saying when you say it.   They are attune to your way of thinking so your arguments make sense to them and they sound persuasive.   In order to do your job effectively you need to especially consider arguments from people who are not attune with your way of thinking and who are the least persuasive.  Their objections will make your writing more persuasive. Persuasive writing is able to answer questions from anyone no matter what point of view and present arguments in a way that everyone can understand.   Everyone you attempt to communicate with may not agree with you but they will consider what you have to say.