You may have wondered how people come up with Original Characters with a functioning personality in the past. You may have also left your mouth agape when you saw someone have their Original Character react negatively to a spider at one moment, then hug their spider anthro friend in the next. Well, it's really a simple process that requires one thing so rarely used these days; thought. I'm expecting you have a general idea of your character at this point and are seeking to deepen or improve their personality now. If so, you can skip a few steps.
Step one: Build a base for your character.
All things are built on a strong foundation.
Find the center of your character's mind, their motivation in life, and their drive to keep breathing (if that is indeed what they do; not all characters are human).
Something simple like "Survival," will more than suffice, as an existence like this will lead to self-conflict of yearning for a higher existence, and thus, to a deepened personality!
A few other things you can use, albeit generic, are; Revenge, Fear, Adventure, Pleasure, Greed, Envy, God, Servitude, and the like.
Also, imagine how your character's race will affect the potency of this drive. Humans are dependent upon a drive for purpose and a desire to live, an alien race may not be like this.
Another important factor to consider is events and people which might have a heavy influence upon your character's self-decided purpose after it is set in stone. You may want to consider slowly but surely changing your character's drive as your story continues, should you so choose. This will surely lead to a more interesting read. (Added by DragonofAether)
Step two: Build upon your base.
Set up their life.
Decide what family they had, if any. The sizes of family can vary from limitless energy beings, to entire colonies, or a simple American family of four.
Give them a place to live, or a lack thereof, and make them a living thing. Your choices are truly beyond your comprehension. Take the size of the universe, of all existence, and multiply that by all the time that has come, is, and will be. That is less than the amount of choices you have!
Step three: Add some furnishings.
What can truly change your character is the little things.
What's their gender?
Their race? (<-- Note this will apply to humans and possibly to alien races. Humans divide themselves into races like Asian and English, this is the context I am using. I am not saying Human or Qiqirn)
Their appearance? (<-- may be affected by step four, events, in ways such as physical scars)
What do they like? (<-- will most certainly be affected by drive and step four)
Who do they care about, or do they even have the capability? Who is their hero, do they even have one?
This can be a challenging step however and is VERY easy to screw up! You're limited here by your prior two choices.
If they're driven by God, will they truly care about their appearance? No, they won't!
If they were born in space and went through a traumatizing experience with the waste ejection system, will they love grass and the planet? No! They'll prefer to keep clean in a metal ship!
Consider all prior choices here, Victorian furniture in a modern home is ick, and vice versa. If you get what I'm saying.
PLEASE NOTE: STEP THREE AND FOUR ARE DEPENDENT UPON EACH OTHER
Step four: Weather your structure.
Everything experiences all forms of emotions. Even simple-minded animals gain a memory of what their masters did to them, and act accordingly.
Don't just put one important event like "and then the evil Dr. Malu impaled Drake's father before his eyes!" While that is a viable choice, you have many more to take advantage of to make you character a living mind!
Give them an innocent childhood, or take it away.
Decide when they mature, at what rate, what they become, and what causes all of it.
If they have special powers, consider when and how they get them, and how it will affect them as a mind.
Put events in their life that will change the course of their life, or simply disturb them in a half-suppressed way until they're six feet under.
Some tips for you, weary traveler.
"You gave me some good examples, but how do I figure out a drive of my own that's original?" Psychology my good man! Examine yourself, or others around you, and look deeply into your subject personality. What is the cause behind a habit of theirs? What makes them hate one person in particular? Why do they have their phobias? Extract it from that personality, and use it as your base for a new person!
"I'm having trouble imagining how an event would affect my character. What should I do?" There's yet another simple process for this as well.
a) Imagine the phobias or likings it may develop. Being bitten or stung by a bee at a young age multiple times may lead to insectophobia, just as well as playing with friendlier bumblebees may lead to a liking for insects. Think of it the way a child would, because childhood is when the basis of a human mind can be seen. During adolescence, people become too embarrassed to show who they are inside.
b) Imagine what subconscious effects it may have on your character. These can be as simple as becoming an angrier person from childhood abuse.
c) Compare all of this to WHEN it happens in your character's life. You may have noticed all of my examples are during childhood. That is because events during childhood are much more likely to deeply effect a person. Note this applies to HUMANS ONLY. If your character is apart of your own original race, you will have to build their base psychology, which is a real challenge to do well.
"This is all really confusing me. Maybe I'll just make another generic 'I'm sad' emo character." GTFO! If it's confusing you, just write your ideas down or put them in a notepad on your pc or mac. It's not always easy, based on your character's complexity.
"You seem to have left out a lot of aspects of a person. Why?" I'm expecting you're already pretty knowledgeable on on how a mind works. Chances are if you didn't think on an aspect of a person, it's not all that important, and can be left out. When you decide what a person does, it is slightly influenced by you, and thus the subconscious aspects are provided by you. This is where a part of relating to a character can come from! We're all human, and thus all original characters will be partially human too! How do you think you feel like a robot while reading a first person perspective book about robots?
"He's/she's only a minor character in the story, do I really have to put them through this process?"
No. The more minor characters are usually the center of attention, or just in the scene of the story, for just a short while. So the whole reason they exist is to pull an elevator lever, or to tell off your main character(s).
"Do I have to do this to make a good story?"
Pffffffft! Of course not! You can easily make a good story without worrying about your characters so much. This is a lot like in the older days of writing when characters were named for their part in the story and obsessed with one thing. My own "Blinded by Dreams" is an example of that style of writing, whereas my fanfic "Hyuponia, Kingdom of Sorrow" involved a lot of psychological thinking. There are better examples though, none of which come to mind at the moment.
A word of warning... and of encouragement.
This is a very long and hard process, but it is well worth it. Because at the end, after all the studying, thought, and creation, you will know your character inside and out! Remember, you do not create the story, your characters create it for you! Kind of like how God made us, and now we're out of his control, huh? (No Sacriligious comments please. If you're an Atheist, take this as a joke, please.)
I wish you the best of luck in your writing endeavors! If you think you're too slow after having worked on one character for months, you're not. You're doing a top notch, high quality job! Keep pushing forward until you're done, and your story (if given a decent plot) will be great!