A good place to start is to use an experience you've had in your life. Personal experiences are unique and easy to base a story around. You can use an event from your childhood, high school, college or the family home as a launching pad for your story. If nothing special comes to mind remember something that happened to you or a friend and imagine a different outcome. What if your date never showed for the high school prom? What if you had broken your neck rather then your arm when you fell out of the tree?
It's easier to write a story about a topic you are familiar with or that interests you. You won't need to research as much and will enjoy the writing process more. If you're a plumber by trade, why not change the setting and compose a story set on a spaceship. If you're interested in dogs you could write a story about how an abandoned dog is rescued by a grumpy old man and improves his life.
Base a story around a good friend of yours. Think about his characteristics, his flaws and his qualities and place him into a difficult situation where he is tested. How would he react to his spouse cheating on him? What would he do if a civil war broke out or their city flooded? What would he reveal about his true nature in a life-threatening situation?
Another source of inspiration are dreams. They don't always make sense but some dreams contain interesting events that you could reshape and base a story around. For example, if you dream about being chased by a shadowy figure you could turn that into a thrilling murder mystery story.
Every story has a theme -- what the story is about -- in contrast to the plot which is what happens in the story. Themes can include honesty, sacrifice, the danger of having unlimited power, love, slavery and many more issues that people have varying opinions on. You could chose a theme you like and write a story exploring it. For example a story in which a son devotes all his time and energy to his ill mother is about sacrifice.