Elaboration Likelihood Model

Description
There are two ways we make decisions and hence get persuaded:
When we are motivated and able to pay attention, we take a logical, conscious thinking, central route to decision-making. This can lead to permanent change in our attitude as we adopt and elaborate upon the speaker’s arguments.
In other cases, we take the peripheral route. Here we do not pay attention to persuasive arguments but are swayed instead by surface characteristics such as whether we like the speaker. In this case although we do change, it is only temporary (although it is to a state where we may be susceptible to further change).
One of the best ways motivating people to take the central route is to make the message personally relevant to them. Fear can also be effective in making them pay attention, but only if it is moderate and a solution is also offered. Strong fear will just lead to fight-or-flight reactions.
The central route leads to consideration of both arguments for and against and a choice is carefully considered.
People are more motivated to use the central route when the issue has personal relevance to them. Some people have a higher need for cognition, deliberately thinking about more things than people with a lower need. These people with a higher need for cognition are more likely to choose the central route.
When they are feeling good, they will want to sustain this and will avoid focusing on things that might bring them down again, so they take a more cursory, peripheral route. People in a negative or neutral mood are more likely to take the central route.
So what?
Using it
If you have their attention, be logical and present a compelling argument. If, however, they are not really paying attention to you (and you can deliberately distract them), put them in a good mood (eg. with a joke) then use subtle cues such as attractive clothes and leading statement. Then quickly lead them one more step at a time to where you want them to be.
Defending
Learn to pay attention to how you are making decisions. In particular, pause when you are about to make a commitment (and especially if it means signing a legal document). Think back about how you made your decision. Was it reasoned, or did you somehow seem to arrive at the point of commitment without much conscious thought (perhaps being distracted by the other person)?