Emotions generally require a 'how' and a 'why.' HOW are the emotions expressed, and WHY does the character feel that way in the first place.
According to some psychological studies, all people can indentify three basic emotions: happiness, sadness, and anger -- or love, sadness, and hate, when you phrase things actively. Let's look at some common reasons for these:
I love you because...
you fulfill some need of mine
I like something about you
of no reason in particular, I can't explain it
we share a common bond
I hate you because...
you hurt me
you hurt someone or something I love
I'm supposed to hate you according to...
The Powers That Be
my conscience
you repulse me, you rub me the wrong way
I'm sad because...
of no reason, I'm depressed
someone/something I love was hurt/damaged/killed/destroyed
I can't do what I love anymore
no one loves me
things aren't good anymore
Love, as we can see, is obviously based on some common attraction -- either that of like, or complement (thus the saying, 'opposites attract'.)
Hatred is basically based on pain, and a need to remove that pain by inflicting it on others.
Sadness is based based on loss and emptiness without emotional support.
Complex Characters
Of course, characters usually feel more than one emotion at a time, either in opposition -- for example the classic 'love-hate thing', which has reached from Petruchio and Kate in The Taming of the Shrew to Tracy and Hepburn to yes, Xander Harris and Cordelia Chase of BtVS -- or in parallel -- the classic confused character, such as Hamlet or Macbeth, pretty much all of Woody Allen's roles, and Xander with respect to Willow Rosenberg (Yes, I'm on a Buffy kick for a while...ok, probably a couple of years...but you haughty lit types can press the panic button and get blown out the escape hatch if you have a problem...my site...MINE!) -- or in combination -- the classic complex emotions of guilt, pride, loathing, etc.
It is important to remember that real people, normal people, probably have all three of these going on at once, in various facets of their character. So to create more realistic characters, the writer must necessarily make them more complex...and then more complex, again.
How complex are we talking here?
Well, consider that each character should have four to eight Schticks.
Each Schtick will have all three of the basic emotions, love, sadness, and hate.
Each of the emotions will exist in opposition (love-sadness, love-hate, sadness-hate), in parallel (love, sadness, hate), and in combination (whole Pandora's box -- guilt, pride, grudging respect, rivalry, jealousy, and on and on...).
So this is (4 to 8) x (3 + 3 + 3 + 0-?) or 36 or more emotional combinations. Per character.
So how do you make a character seem real without going through all this drudgery?
Acting "Out of Character"
Simply put, you cheat. (Always a good solution when faced by unfair odds.)
You have your character act abnormally -- "out of character." Usually, this shouldn't be a drastic thing, or else you'll probably lose your readers' sense of disbelief. But when combined with a good plot-twist -- especially the double-reverse plot twist -- it's really effective and cool.
The trick is justifying it logically.
You can bring up some aspect of the character's unknown past (for example, the whole Angel/Angelus curse thing on Buffy.) This is very easy, and useful for mysterious and/or long-lived characters. It can blow up in your face, though, if you don't keep good notes to keep track of it...the Star Trek book series is famous for little inconsistencies. On the other hand, it's really spectactular when you pull off a massive, complex, interwoven past...look at Babylon 5 if you have any doubts to the truth of that.
You can go the 'sudden realization' or Zen route, which makes for great drama. All of a sudden, the world is crystal clear in your character's eyes. She knows what she has to do, and does it. Of course, you can't do this often, or else it becomes mudane. Besides, who has Zen insights on a regular basis?
Or, you can chicken out and just say nothing. This is cheap, but can work if you use it to build a temporary sense of mystery. But, the description of the scene must be clear and intense. The aim with this route is to make the reader go, 'WHAT THE HELL..?', so it must be set against a completely consistent and believable background, against which it contrasts like a nova. The end scene of the movie The Abyss is the best example I have ever seen of this technique. This scene gave me a two-hour high -- it was that awe-inspiring.
Normal Emotional Characterization
Of course, to do this, the character must have some emotional norm to deviate from.
To establish this, all you have to do is tie each Schtick to one or more relationships your character has with the other characters. I read on someone's website that "character longevity is based on the amount of relationships [that connect a particular character to others]", and this also applies to emotional range and realism. That is, the more people the character knows, the more complex he can be.
The Character Motivations page
Other writing resources:
Awards Page
Character Breakdowns & Analysis
Fun With Profiling:Buffy the Vampire Slayer
How to Write
Motivations by Age Type
More on Schticks Page
My Attempt to Figure Out Relationships
Page
Palaskar's Primer on Emotions for Characterization
Wants & Needs