Take the article one section at a time and ensure you understand the section before moving on. Sections may vary by academic discipline, but common sections include the abstract, introduction, methods, results, conclusion and sometimes a discussion. Start with the abstract, as it gives a summary of the article's purpose, methods and conclusions. This will give you a general guide for reading the rest of the article. After this, identify the rest of the sections in the article, which journals often designate by a subject heading.
Read slowly through the article and ensure you understand each section -- and each line -- before moving on. If there are words, phrases or jargon you do not understand, look these up before moving to the next section. The Internet is an ideal resource for finding basic information in these areas. For instance, if the text you're reading includes experiment results that report a P value, look up what a P value is and how to interpret it. (For the record, a P value is the probability of an event or outcome in a statistical experiment.)
You can often bolster your understanding of the article by discussing its meaning with others. First, summarize the article while identifying key points and areas of interest to you, without copying the abstract. Then, discuss your understanding of the article with one or more people who have also read the article. You can often identify areas of misinterpretation and confusion by having to verify your summary with another person.
Reading just one article will not give you a concrete understanding of scientific literature. Instead, read a series of articles and compare how the articles were written, the writing style, the experiment's methodology, and how the authors reached their conclusions. Instead of reading articles from different disciplines, choose articles relevant to your field of study and in subject areas that interest you. This will help increase your motivation to read. In addition, follow a line of research backward by looking at each article's list of references and reading the articles cited. This will help you trace the evolution of a topic and help link the articles together in a meaningful way.
If you have ideas or questions about the article that were not addressed by prior research in the subject area, contact the corresponding authors. Be professional and courteous in your communication to the authors, and demonstrate a comprehensive understanding of the article. Do not contact authors with simple questions, such as those you can look up in an encyclopedia or scientific journal. Instead, ask questions that require some thought to answer. Authors are often experts in their fields who stay busy, so do not expect a quick response -- and sometimes you may get no response at all. However, it is still worth trying.