Read essays. The most important part of introducing a form is to become familiar with good examples of the form. There are many good anthologies of essays as well as whole books by individual authors. Reading examples of essays that are similar in form or content to those that will be written is always useful. To know how to read an essay is the first step in knowing how to write one.
Address different forms that an essay can take. Essays written in an academic setting most often take up a sustained argument about a specific topic, proposing a thesis and arriving eventually at a conclusion after justification and evidence. This is only one form an essay can take. Essays can simply reflect on personal experience, compare and contrast related things or simply analyze intensely. Choosing the correct form for an essay is a critical part of making the essay effective.
Introduce essay writing as a process. Composing a well wrought essay usually takes several steps. Whether the essay is prompted by a specific purpose or not, there always needs to be some brainstorming about what the essay will actually address. After that should come some research to find relevant information and some sort of organization of that information. Information is often organized through visual diagrams and multilevel lists that make it possible to map out the different sections of the essay.
Write the essay. Sometimes the best way to find out what the essay will be about is to simply write it. It isn't always important to know exactly where it will end up. Depending on the kind of essay it is, sometimes it's useful to do a pre-write simply to address the topic on paper. These can make use of the research and brainstorming that took place in the previous steps, but don't necessarily result in a finished product.
Rewrite the essay. It's best to read the essay all the way through out loud if possible. This gives the writer a better idea of whether the piece is coherent and clear. Proofread for errors and ambiguity, and correct. This step can be repeated indefinitely until the essay is satisfactory and effectively achieves its goals. No piece of writing is perfect initially, and no writer is perfect. Everyone needs to rewrite and the more essays a person writes of different kinds the more effective their writing will become.