Explanatory writing is easily recognizable in books such as encyclopedias. The writing aims to explain a certain topic to the reader to promote an understanding of how it works and what it is. Another example of explanatory writing is a textbook, which explains the basics of a subject to a student.
Choose a topic you are comfortable with and write an explanatory non-fiction piece about it. Use a clear, even tone like the one in an encyclopedia or textbook. Leave out emotive statements and literary rhetoric, leaving only the facts explained in a clear, concise fashion.
Instructional writing aims to show the reader how to perform a task. Examples of instructional writing can be found in recipe books and instruction manuals. The writers use active verbs such as "chop" and "press" to tell the reader what to do.
Read through examples of instructional writing (see Resources) to gain an understanding of the medium. Practice by composing a guide to any task with which you are comfortable. For example, you could write about how to change the brake pads on a car or how to play "Black Betty" on a harmonica.
Persuasive writing is all around us. The most basic examples can be found in advertisements. Persuasive non-fiction isn't unbiased in the way that explanatory or instructional non-fiction is. Instead, it uses emotive phrases to exaggerate the benefits of a product or viewpoint. Politicians are another reliable source of persuasive language, and the rhetorical techniques they employ are the essence of persuasive writing.
Persuasive writing is assured, emotive and one-sided. Write an advertisement for a product or a speech for a politician to practice your persuasive writing skills.
Writing that aims to discuss an issue is another type of non-fiction. Examples of discussion-based non-fiction can be found in editorial sections of newspapers (although they may also be persuasive), essays and reviews. Discussions aim to present both sides of an issue, explore the evidence for each, and then weigh the positives and negatives. He goal is to present both sides of a debate.
Practice this by writing an essay on a chosen subject or by reviewing a product. Be unemotional, fair and reasoned in your writing. Aim to present both sides of the issue and let the reader make up his own mind.