For me, I start with ideas. I brainstorm as I'm walking along or going to sleep or taking a shower. Come up with a bunch of ideas. Then I let them grow in the back of my head. Put them away, revisit them in a day or two and see what happened.
Once I have a basic concept down, I go further. I start from the point of view of character growth. What do I want to happen to the characters. How do I want them to change and grow. For me, any story is first and foremost about the characters and plot should be approached from the viewpoint of how it moves them through the story.
Then I do a roadmap. Roughly, where do we start. Roughly, where do we end. what points do we want to hit along the way? Only then do I really think about the beginning of the story. What tone do I want to set? What characters do I want to introduce? What do I want the reader to get right off the bat, what do I want to tease them with?
The first page of Mysteries of the Arcana, for example, starts with a photo scrap book being burned. There are four pictures. One shows a little girl on her daddy's shoulders. Another shows the same girl, older, being taught to shoot by her dad. The third shows the same girl, much older, hugging her dad goodbye. He's in a military uniform and there's a bus in the background. The last shows her accepting a flag from an officer at a military funeral. There's a text box reading: I didn't leave a note.
I wanted that first page to tell a story. I wanted the first page to give a good, solid introduction to the character. Readers get a quick snapshot of her life story, though not all of it, and they hear her voice as she says she didn't leave a note. That, combined with burning the book sort of should suggest either running away or suicide right off the bat.
The story moves from there. I show her walking through the tunnel in the equivalent of the opening credits of the movie. Narration over setting shots to establish the initial tone. Dark. Damp. Somewhat depressing. First person narration so the reader can more quickly identify with the character, who will serve as their point of view character. As she learns about the strange multiverse the story takes place in, the readers do.
Then BAM! Elf fighting robot. The first pages were about the character, Theresa. We learn about her, learn she's going to kill herself. Learn she's thought a fair amount about it and wants to do it right. Then we end her narration with her wanting to die with that shot. Elf and robot fighting. We introduce the fact that this world has magic and super science. Just like she's thrust into something strange that derails her suicide plans, the reader is thrust into something strange as well.
By the way, I want to emphasis the importance of research. In this case, I read a lot about suicide and teens, especially teen girls. That research was folded into the narration. Girls usually choose less physically violent methods of suicide. Boys usually pick more violent (and often much more succesful) methods. I made sure to point out that Theresa wasn't going to use gentle methods. No pills. No razor blades. She knew those didn't work as often as a bullet did. Just like Theresa's hair and clothes, her chosen method for killing herself was designed to show her tomboy nature.