I have never worked with APIs before (and have very little programming experience outside of HTML and CSS) and I am struggling to find any clear tutorials or explanations.
In his excellent book, Practical API Design: Confessions of a Java Framework Architect, Jaroslav Tulach makes a convincing argument that the API of a system really consists of all the things (function signatures, exposed objects, configuration file formats, etc.) that you have to know in order to use a piece of software.
To your specific questions, there are no universal standards for how APIs should be designed; styles and practices vary wildly between programming languages, language communities, organizations, etc.
To get started, find some library in Your Favorite Language, and look for code samples that show how to exercise all its capabilities. Then try playing with those samples to vary their behavior.