Okay... I'll try to explain it to you easily,
An expository essay explains a factual main idea, an opinion, or personal insight.
A single paragraph is just that: One paragraph on a topic. It could be descriptive, persuasive, reflective, summative etc. Use the different colors and paragraph templates from Step Up to Writing to help identify beginning/ summary, arguments, and support sentences. Green for topic sentence, yellow for a reason, detail, or fact, red for explanation or example, green for summary sentence. This is the simplest pattern. The 5, 6 or 7 sentence accordion paragraph templates are for more difficult paragraphs . Special paragraphs could be compare/ contrast, sequencing , problems/solutions, persuade and convince etc.
Brainstorm first, then organize information before writing. You can use the spider web method, shapes, or the more traditional outline format. Then write.
For multiple paragraph essays: Develop your thesis, idetify key points to prove the thesis, provide examples to support the key points, conclude by summarizing and/or offering readers a reason to take action. This is more like extending the accordion paragraph, so do NOT stack accordion paragraphs. Tie everything together with transition word and phrases.
Once you have the first draft written, revise the ideas, then edit for mistakes in capitalization, punctutation, spelling, word usage etc. Finally, do the last good copy. If you work on a word processor, use the tools to help you with editing. Proofread the final paper, make sure it is ready to hand in.
Whew... a semester course in 100 words or less. I hope you got enough information. If you have a specific question, you are welcome to try again. I have the Step up to Writing manual at home, so I can look things up.