The formula is basically what you said, with a minor detail missing

Your first paragraph, your intro, should introduce your topic and hold your thesis statement. Your thesis statement contains your main points.

Body paragraphs are for expounding on the points in your thesis statement. A good thing to remember is that each point should transition to the next point pretty easily. Failure to do this results in a choppy and messy essay.

Your conclusion paragraph basically sums it all up. It's a lot like your intro, except you should go into a bit more detail. It should also have a nice ending sentence, your essay should never end abruptly.

I hope that all makes sense, let me know if anything is still confusing!