Here are some techniques that will make you much more persuasive.
Persuasion is all about emotion
Despite how we’d like to see ourselves, humans are fickle and will decide how to act based on how we feel. Logic is rarely used to make our decisions, and typically is used justify them afterwards. This is true even of people who want to hear all the statistics and figures, because behind those facts is a desire to be seen as rational, or the exhilaration that comes from getting it right. 
Even when it’s about facts, persuasion is still about emotions.
Let people indulge their pleasing self-perceptions
We all see ourselves as kind, intelligent and perceptive. Even pricks and idiots. Too often when trying to convince someone to change their opinion, people will seek to prove that your opinion is wrong (and therefore, by default, theirs is right). Don’t do it. It’ll almost always turn a discussion into an argument, and whoever they’re talking to will look for fault in what you’re saying (or who you are) rather than addressing whether you’re right.
Start with your listener. Work to establish your answer as the rational choice that perceptive, intelligent and kind people would make.
Establish common ground
Talk with people, get to know what they value, what they know, and a bit about what they’ve experienced. Speak to that, particularly around areas which you have both experienced. 
We like things that are like us. Establishing this common ground, in matters of morality or knowledge, or even a similar upbringing, makes your opinions seem more valuable and reasonable. It will also build a rapport with your listener, as can smiling and being friendly. Once you’ve developed that rapport, you may just choose to talk how much this thing means to you, and they might agree, just to make you happy.
Ask questions
Get to know a bit about them. Too often, in campaigns to convince someone of something, we rush straight past this bit. Talk less about your solution, and more about the person. The theory of evolution is a very different proposition if you’re talking to a child who’s never heard of it, compared to a dedicated adult creationist. If you’re about to ask your boss for a raise, finding out what they value (punctuality, results, personal relationships) will make you much more effective at persuading them. 
We all see ourselves as fascinating, and when someone asks us questions, they confirm that belief, and that makes us feel all warm and special on the insides.
Your questions can also probe at the tangled web of influences and restrictions and pressures that someone else may be ensnared within. Your creationist friend might talk about an overwhelming social pressure to conform, just as your boss might be under pressure from a board of executives to reduce costs or start firing people. Knowing what these pressures are will help decide when to open the discussion, and what to talk about when you do.
Be flexible
Once you’ve asked a few questions, established your common ground, developed some rapport, and presented your opinion as the rational, intelligent, kind choice; be willing to bend. When we are faced with someone whose opinions are intractable, we will often mirror that and become inflexible ourselves. To get the conversation going, be willing to accept changes to your ideas. 
Their input into shaping your goal will make people far more inclined to make it work, and you never know, they may even make it better. Your boss might not want to give you a raise, but they may be willing to invest in furthering your education, or find more exciting work for you to do.
Know when to apply pressure
It’s important to know when to up the ante. Applying timely pressure can push people into making decisions, which is why salespeople always ‘need to know by the end of the day’ because ‘someone else is looking at this’. 
Humans have an innate fear of missing out, and value things relative to their scarcity. To push people into making decisions, you can apply external time constraints, or introduce them to their competition. This method can be sleazy, so don’t push too hard.
It’s also important to recognise when you have the power. If you’re in charge and are spending your time convincing people to do something you could be ordering them to do, you may actually find they start to lose enthusiasm for it. In their heads they’re asking “Why are they trying to convince me?”. This raises another important point: 
Know when to release the pressure
When people are convinced, offering further arguments can actually weaken your position. If someone has heard a good reason to agree, then they hear another, less good reason, they’ll often end up focusing on the weaker ones. Persistently pressuring people can sometimes turn them off, particularly if they feel they might be about to make an irreversible decision (that fear of the road less traveled again).
Ask them
This one is devastatingly simple, and so often overlooked: Ask them!
If you’re set on an outcome and someone isn’t on board, ask them “What would change your opinion on this?”. They’ll lay out a course of action for you to convince them, and in doing so, they’ll start to convince themselves. At very least, they’ll have given you a detailed step-by-step guide to persuading them.
Sometimes, upon attempting to answer that question, they will realise that nothing would convince them, which is also pretty important to know. Inflexibility is a trait of an unintelligent person, so as soon as they’ve recognised their own inflexibility, they’ll usually be keen to change. If they aren’t, it’s still useful to know when to save your breath.
Persuasion is all about changing how people feel. Rather than convincing them that they should agree, find a way to make them want to agree.