People have a lot of different tactics to get a story started. Some people make an outline of their plot and characters and write from that; other people just start writing when the mood strikes.
I think it helps to have a very firm grasp of your characters and who they are, and let their unique actions drive the plot.
In some genres, the plot kind of drives itself. Like in swords and sorcery fantasy, the good guys go on an epic journey and fight the big bad guy. Or in a horror movie, they all get chased around in the woods and killed one-by-one.
You can throw a twist into a typical genre story by giving the characters strong, realistic personalities. Let their choices stem from their unique personalities, and let that drive the plot.
For instance, there’s the “hero goes on an adventure and slays the dragon” story. The hero generally has to be brave and selfless, or they wouldn’t have taken this mission in the first place. The plot of this kind of story usually goes by the numbers. The hero sets out from home, joins up with a rag-tag bunch of companions on the road, they overcome obstacles, and they have a final showdown.
If you change the main character, you can change the story. For instance, maybe the main character isn’t brave at all, but they’re clever and resourceful. Bilbo in “The Hobbit” is a great example of this. (I’m not talking about the movies, which seem incredibly silly and pompous. The book is an awesome, classic adventure story.) Bilbo isn’t a typical adventure hero, charging in with a sword to fight the bad guys. He gets into and out of trouble because he thinks outside the box and he’s willing to be sneaky, but over the story he develops genuine courage and uses it. The story follows the classic adventure format, but surprises you along the way.
You can also have the characters get into trouble when they give in to human failings. For instance, a character might have a moment where they’re genuinely selfish, lazy, petty, etc., and their decision changes the course of things. (The movie “In Bruges” is great for this. It’s about two hitmen laying low in a quaint tourist town in a job gone bad. Just about every plot point comes from Ray’s impulsive nature or Ken’s thoughtfulness. Watch it; it’s so great!)
Game of Thrones is another great read for character-driven storytelling. There are lots of 3d characters acting in their own self-interest, and that eventually leads to a civil war. There’s a saying that every character is the star of their own story; Game of Thrones makes this literal by giving everyone a point of view.
One thing I really like to do is write short, random nonsense about the characters bullshitting around in different situations, just to see how they would act. It’s a fun way to blow off steam and it lets you get to know the characters and their personalities. With the main characters in my novel, I’ve written external short stories from unrelated plot lines, sort of a remix of the main story. And I’ve also written random conversations where they meet in a bar, or where everyone is living in a different time period.
The best way to get better at writing is reading and writing. Good luck!