Typically, a story should have a plot (although there can be exceptions). This is much easier said than done, though. I know quite a few writers who can write the hell out of a scene or really set up a situation, but that's about it. A plot is so much more than that.
If you are new to writing, there are a few basics you should probably know about story structure. First, there is a beginning, middle, and end (although not always in that chronological sequence). Second, there are usually five components of a plot arc: set-up/exposition, rising action, climax, falling action, and denouement/resolution.
Set-Up/Exposition - This is where the characters are introduced and the situation is set up for the reader. It's important to catch a reader's attention here, because she could easily be checking her Facebook account or tweeting, rather than using her time reading your story. Hook her with the first sentence and guide her into the story.
Rising Action - Imagine a pot of water being placed on a hot stove. Rising action is just the water heating up quickly. This is where the obstacles start to slam your protagonist. Keep in mind that if it's not heating up, then you're not cooking with your story.
Climax - The pot is now boiling! Your story is now at the highest point of tension. What's going to happen to your protagonist? I have to know! This is so intense that I'm going to finish this story before I respond to these damn tweets.
Falling Action - This is what the protagonist's response is to the climax. Imagine that you're taking the boiling water off the stove now. It is still hot, but it's cooling down. The story is steering itself towards an ending.
Denouement/Resolution - This is the conclusion to the story. What happens to your protagonist? Is it satisfying? Maybe it's shocking. Maybe it's open-ended. Regardless, the water is now room temperature--that is unless you're the type of writer who likes to take the pot of water off the stove at the last possible minute.
The most important thing to remember about plot is that you must have conflict. Since all major characters have motivations, the key is having those motivations have conflicting results for other characters. For example, you're in my class and want to make an "A," but I'm required to grade using a curve that only allows me to give out five "A's." Our motivations are different, and as a result, the seeds are there for possible conflicts. But conflicts don't have to just exist between characters. They can be internal struggles, battles with nature, etc. The key is that you have to put your protagonist (to reuse this metaphor) in some hot water.
The irony is that most writers are conflict-averse. I can't stand arguing or getting into messy situations, but for the sake of my stories, I have to at least put my character to the test.
One last point on plot. Know exactly where to start your story. Start as close to the action as you can. In fact, your story should already be going by the time you write the first word. It's not necessary that we see your character wake up and get ready for work--unless that is absolutely necessary for us to appreciate the conflict.
In the beginning, writers created motivation for their characters and, having done so, gave birth to stories.
Okay. Enough of the scriptural prelude.
While a lot can be said about characters and characterization, I would be remiss if I didn't start with the protagonist. Many people refer to the protagonist as the good guy, but I don't really believe in good or bad people, especially when it comes to literature. The best characters aren't stock or fill-in-the-blank characters; they are ones that make decisions that may or may not have adverse effects on others. It's kind of Zen-like when you think about it: characters define themselves by what they do. As such, a protagonist might best be described as simply "the main character," the character who enters the hero's journey or seeks to find something. And in keeping with the disposal of good and bad, the antagonist would simply be the character with a motivation that runs directly opposed to the motivation of the protagonist. These conflicting motivations give rise to conflict, which is what gives rise to plot (but that's another discussion altogether). *Note: Conflict is not just the effect of character on character motivation; it could arise from a number of factors, including nature, self, or a higher force.
If a character goes through changes, or is dynamic, he is considered round. That simply means that the character at the beginning of the story has evolved by the time the resolution comes. More than 90% of the protagonists in literature are round.
Flat characters are the opposite of round characters in that they are static and don't change. Hollywood tends to play with this type of character in movies that involve people with mental disabilities. While a mild argument could be placed on Raymond from Rain Man being round, he's actually much more of a flat character. As a result, flat characters tend to be accompanied by round characters. Just look at Forrest Gump. He had Jenny and Lieutenant Dan to balance him out. And Lenny had George in Steinbeck's novella Of Mice and Men.
Stock characters are best described as characters that, once they are seen, the reader automatically knows what role they serve. Just think of cowboys with white and black hats.
A final category of characters are archetypes, which, in the wrong hands, can become stereotypes. Each culture has its own archetypes. With African-American literature in particular, there are a number of them: the sambo, the mammy, the tragic mulatto, the bad-ass, the buck, the militant, the sapphire, and the list goes on and on. Just one look at a TV show like Good Times, and one sees many of these archetypes on full display. At one point in time, archetypes were original character types, but history has shown us that readers tend to respond to characters whose traits are recognizable in some way, so now archetypes straddle the line between being rehashed character types and stereotypes.
While a lot more could be said about characters, the main thing to remember is that they are representations of human beings (which is a pretty heavy notion when you think about it). Everything else is just a way of explaining how a character functions within a story.