The summary goes after the title page, on it's own page, separate from the main body of the paper. This gives your reader a quick, handy overview of the topic. Think of it like the jacket copy to a novel, which is written concisely and has enough information to get a person to buy the book.
It's a good idea to write the summary after the paper has been completed and not beforehand as this might color any conclusions you might make.
Depending on what manual of style your professor wants you to use, you'll be either writing a summary or an abstract. It's just two names for the same thing. For example, if you use American Psychological Association (APA) style, it's an abstract. For other styles, like Modern Language Association (MLA) or Chicago Manual of Style, it's a summary.
In the business world, it's called an "executive summary."
Your summary should be between 100 to 120 words, in paragraph form, and no more than a page long. Summarize, don't over analyze. The summary should only contain the key points of your paper; don't add anything to it that isn't there. If you do, you risk misdirecting your reader.
Economize your words, but don't abandon the rules of grammar for the sake of brevity. Use complete sentences. Write the summary in the past tense since it is an overview of work done. It should stand on its own. Don't refer the reader to a table, chart or factoid deep in the body of the paper. Save the background information for the paper itself.
A good summary will either make or break your paper. If it's written well, the reader will keep going. If it is poorly written, the reader, or professor in many cases, might put your paper down and move on.