Well, coming from an aiming-to-be-author, I normally start by building the world first. Is it set in real life or a made up world entirely? When I have no starter ideas for the world I personally just make whatever comes to my mind first. Same with genre, honestly.
Then I build on other things such as (whether in a fictional world you made up yourself or a fictional version of the real world) religions or organizations, maybe species as well if you're a fantasy, sci-fi or horror writer.
With characters, I normally focus on making what will be the antagonist or 'villain' of the story first. If it's a person, don't just make them evil off the bat. Give them a reason. Were they betrayed? You know, the usual. The antagonist/villain doesn't necessarily have to be a person. It could be a disease or something. Depends on what kind of story you're writing.
Then I focus on main characters. Now, I don't exactly know if I can give actual advice for this, since everyone probably makes their characters differently. I, however, normally make the main character have some kind of ties to the antagonist/villain, if a person, rather than making them just hate them on the bat. Like, maybe an old friend or even a family member. Just go with the flow, that's what I do.
Making a story is kind of like going down a new river. You never know where it'll lead you until you get there. You just got to roll with it.
Hope at least some of this helps in some way :)
