How we change what others think, feel, believe and do
A simply way of understanding motivation is to consider the gaps that act to drive us.
A gap requires two things, between which that gap can exist. For motivation, this can include such as:
Leon Festinger described Cognitive Dissonance, where the gap between two conflicting thoughts lead us to seek ways of reducing this. When we simultaneously think about what we want and about what we actually have, we feel a similar discomfort, often as a physical tension.
Gaps are also the driver for disagreement between people. Where our internal motivators are different from others, then we will disagree with them.
If we have a values gap with others, then we may consider them bad and immoral in some way, or perhaps that they are overly-concerned with something that we find relatively unimportant. And they might think the same as us.
If we have a beliefs gap, then we will disagree on what it true and false. One person may say that something happens like this, whilst the other says it happens like that. Or one says X exists whilst the other says X does not exist.
In a goals gap, I may be seeking to achieve something, but in working towards this, I am preventing you from reaching your goals.
In a commitment gap, I am concerned about the gap between what you have promised to do and what you are actually doing (or are likely to do). People in business spend a lot of time managing such gaps.
To persuade people, there are two things you can do.
Decrease distracting gaps
First, recognize that they are already motivated into doing other things, which means they already have some gaps that are motivating them. So in order to get attention space, find ways of removing the gaps that already exist.
Solve their problems. Help remove their distractions. Help them reach their goals.
You should also reduce gaps around beliefs and values, such that you can find more agreement. Beliefs can thus be traded -- if I agree with one of your truths, will you accept one of mine?
Create and increase the right gaps
When you have their attention (and perhaps at the same time as decreasing the distractions), you can then start making new gaps. Point out things that had not noticed. Show how important things are. Show the implications of not doing what you want them to do. And so on.