I am not sure if you are asking about writing summaries of literary texts or about writing summaries of articles. There are certainly at least five points that can be made about either, and I am going to address some points that are true for both, and some points that are true for each individually.
First, whether you are summarizing a literary text or an article, your summary should be quite brief. One page is about the most a summary should be, no matter what, and if it is possible to summarize more briefly, that is fine, too.
Second, you must provide in your summary the title of what you are summarizing, along with the name of the author. If you are summarizing an article, name the article. If you are summarizing a book, name the book. If you are summarizing a short story, name the story. Even if you are writing a summary as an assignment for class and your teacher knows very well what you are summarizing, you should imagine you have an audience that does not know.
For a literary text, here are some of the points you want to bear in mind:
1. You should always state what the setting is of the story. This means letting your reader know where the story takes place and when the story takes place. For example, The Great Gatsby takes place in New York in the Roaring Twenties.
2. You should always name the major characters in the story. Sometimes a story has many characters, and it is impossible to mention all of them. For example, The Goldfinch is filled with many characters, probably too many for you to mention. But once you have read a book, you can name the protagonist, the antagonist, a love interest, and any other characters that are central to the plot.
3. You should briefly describe the plot of the story, ideally in five or fewer sentences. This is often the most difficult part for people who are learning to write summaries, but it can be done! I might say this about The Goldfinch, which is nearly 800 pages in length:
Theo loses his mother in a bombing in a museum, encounters a dying man and Pippa, who becomes his obsessive love, steals a painting from the museum, and spends the rest of the story either hiding the painting or trying to rescue the painting. Along the way, he encounters characters both good and evil, who teach him valuable lessons about life and morality, which allows him to finally mature.
Remember, a summary needs to be brief!
4. A summary should include some discussion of the theme or themes in the story. Is this a story about coming of age? Is this a story about man versus nature? Is this a story about the American Dream? Whatever themes are present in the literary text, you need to mention these.
5. A summary should include a brief discussion of any other literary elements that you note in the story, for example, symbols, imagery, the author's tone or the point of view of the narrator. These are all aspects of literary analysis that can and should be part of a summary, albeit briefly.
For a an article summary, your focus is going to be a bit different:
1. You must summarize the author's main idea. In a properly written article, this will usually be in the form of a thesis statement. Perhaps you are summarizing an editorial from the newspaper. What is the author's position on his or her topic of choice? You must let your reader know.
2. You should summarize the author's supporting points. Ideally, these will be part of the thesis statement, too, but not always. You may have to read the article carefully to find out what these are. In an editorial that supports amnesty for immigrants, for instance, the author might use statistics to support the points, might use logic to do so, or might provide anecdotal evidence, perhaps stories about immigrants he or she knows. In an article that is summarizing research, the support is going to be found in the research results in the article. Remember that this is not a critical analysis, but a summary, so you are not expected to critique the support, just to summarize it.
3. It would be good to provide some information about the author of an article, such as an academic background or where the author works. This is more important in an article summary than it is in a summary of a literary text.
4. In a summary of an article that is reporting on research, some details about the methodology and subjects of the research are very important. Who were the subjects? How many people were part of the study? Was there a control group? Was it a qualitative or quantitative study? Was it a longitudinal study? For a reader to get a good sense of the article, these are questions that must be answered.
5. In a summary of an article that involves technical terms or terms of art, it is important to explain these for your reader. If you are summarizing an article on operant conditioning, do not expect the reader to know what this is. If you are summarizing an editorial on TPP, which is the Trans-Pacific Partnership that Congress must approve, you owe it your reader to explain what this is. Do not assume that your reader is going to be familiar with technical vocabulary, initials, or terms of art.