Implementing your API involves the assembly of multiple pieces. Here's a little guide that might help you make your way through the underbrush.
I keep my CREATE TABLE statements in a text file so I can reuse them if necessary. If you need help with SQL SELECT statements, it's great if you can easily share your CREATE TABLE statements with me.
In the books/authors example, I would start with my simplest endpoint: /authors with no GET arguments. Ultimately, this endpoint should just return a JSON list of dictionaries, one dictionary per author.
Do your work in little stages, and test each little bitty stage.
And then commit each little bitty stage.
This is me looking out for your happiness. Do it.