A story should always have a plot, regardless of genre. 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.