Start with the purpose
We don't just build an API because it is a fun thing to do. We build APIs to achieve a purpose. They help us or our users do something that we want to do more efficiently. This might seem obvious, but let's be honest: we forget to do this far too often.
Design is a difficult domain. Perhaps your company has designers (as mine does). Technical people such as testers and developers can sometimes dismiss what designers do as "just making things look pretty," but the reality is that good design is very hard. Good design makes something that is suited for its purpose. This book is not a book on designs (if you want to read more about the theory of design, check out books such as The Design of Everyday Things by Don Norman). However, if you are interested in good-quality APIs, you need to think for a few minutes about the purpose of your API and how you will design it to meet that purpose.
Knowing that you need to do something is an important...