Writing an excellent essay, whilst naturally requiring good and convincing prose, is actually quite the regimented science. A good essay 'formula' will consist of the same kind of points and argument styles but shaped to any different essay question. The same goes for the first part of the essay most - the introduction.
To introduce it is paramount to immediately and clearly answer the question! This may sound like an obvious point to make but a good essay will show the marker from the very get-go what your argument will be. By making your argument clear you'll have an easier time demonstrating it to the reader. Once you've 'answered' the question you might need to define some terms in it - for instance my last essay was on 'lynching' in the United States. In my introduction I discussed the issues in defining exactly what lynching is as it has no concrete one. This shows sophistication but it can also be used to make broad words in your question more precise and thereby easier to mould into your argument.
Those are two things I will always do no matter the essay question. The rest of your introduction will consist of consisely listing the main points you're going to make in the rest of the essay. This showcases great structure (if you stick to your proposed points in the essay that is!) and it makes things easy for the marker. An easy essay to read, with clearly outlined points and well defined question terms, is one that always makes getting a good mark more likely.