First of all, a disclaimer. If I really know how to motivate people, this will really be my ticket to financial freedom. To motivate someone, you really need to understand both the science and the art. I've been doing this for 6 years, with varying results. Still trying... Broadly, to motivate people you have to maximise their pleasure and minimise their pain. I'll try to include accompanying examples.
Where applicable, I'll use a common example to illustrate the finer points. The example is this scenario where you are bringing your kid to the toy store. But the kid wants to buy a particular toy which you are not so interested in purchasing.
1. Threat of punishment
It's the classic "If you do this, I will do this" kind of motivation, though the "do" part is more like a disincentive to do certain things. I've always seen parents who said this. It's more a perceived punishment rather than actual punishment. But if the promise of punishment is not carried out, then the threat gets weaker over time.
Example 1: "If you are still so naughty, I'll will make sure you'll get caned when we get back"
2. Lure of rewards
"If you do this, I will do ___" - that's the key point of this method. The "do" is followed by something positive and pleasant. The promise of reward is usually good enough to motivate someone, not the actual reward itself. If the reward is not carried out after the promise, the method gets weaker over time.
Example 1: "If you get 80% of his final year exams, I'll buy you the toy. Do you want to study hard for your exams?"
Example 2: "If you don't make a scene here, I'll bring you to eat ice cream. The weather is so hot, you do love a nice cool ice-cream don't you?"
3. Reduce disapproval
I find that women are better at using this. Humans need to seek approval from significant people in their life - either parents, partners, spouses, friends, classmates etc. By putting your criteria in which you disapprove people, you can put a disincentive for others not to act in a certain manner.
Example 1: "Look at the little boy there who is crying. He is so disobedient and don't listen to his mummy. I don't like kids like that. Are you going to be disobedient like the boy too?"
4. Maximise approval
Same as disapproval. You set your criteria for your approval, then you compare how someone is approved by you because he/she fulfilled the criteria.
Example: "See your brother sleeping in the pram. He's so nice and quiet. I love kids who are quiet and obedient, so please don't make me angry ok?"
5. Appeal to ego/pride/vanity
Self explanatory? A bit similar to approval but the motivation is clearly different. Ego/pride is more internal.
Example 1: "You are such a big kid now, still crying at this age? Look that uncle is laughing at you now"
Example 2: "You are such a big kid now. Big kids don't cry over toys. You don't want to cry over little things like toys right?"
Example 3: "If you cry more, then you will be ugly already. No more pretty face. You like to be pretty right?"
6. Fulfil basic needs
Basic needs of a living thing are the ability to reproduce, to eat, to excrete and to move about. Essentially, this is the need to survive (or the survival of one's genes). This is one of the most important yet primal motivator in anyone's life. Crude but it works very well. In modern times, the need to survive can be rested on one commodity - money. Thus, wanting to earn more money is classified by me as a primal need to survive.
This method is so effective. Just look at what people will do just to survive an earthquake or tsunami.
7. Satisfy curiosity
To discover the unknown, to find out 'what if'...these are motivated by the need to satisfy one's curiosity. It's the motivation that makes one read a book (to find out what happened) and perhaps to finish one whole drama HK drama series in one seating. I suppose scientist are quite motivated by this. It's quite hard to find people who are motivated by curiosity in Singapore, from my experience. It's a rare sight.