Research your topic thoroughly. Look up the references and evaluate the methodologies the author uses to form his conclusions. Find additional articles that support and/or refute those conclusions. For example, if you are critiquing an article on global warming, look up the articles that your author used to support his work, then find articles that support other ways to view the topic. This gives you a rounded understanding of it on which to base your evaluation.
Write an introduction that explains the general issue being addressed. Include general research trends, and how your article fits into them. Be as objective as possible and qualify statements of strengths and weaknesses with possible reasons and proposed solutions for future research.
Consider the author's hypothesis. Write a detailed description of her idea, and compare it with similar research projects. Answer questions such as: "was the hypothesis logical?" "what was the relevance of the project?" and "how does it compare with other similar projects?" Successful scientific arguments depend on the ability to ask and answer the best questions possible. Include a statement about the author's questions, and what additional questions might be helpful.
Evaluate the methodology section. Compare the author's methodology with the methodologies used by researchers in similar projects. Include both strengths and weaknesses in your paper, plus possible reasons for weak points. For example, if limited funds restricted the possible sample size, discuss how that might have impacted the study conclusions.
Compare the author's conclusions with the conclusions in similar projects. Consider the strength of his arguments, and consider whether or not you agree with them. Propose additional conclusions in your paper and what research might be needed to support them.
Write your own conclusion. Include information about the strengths and weakness in the research project you evaluated. For example, if you think that the hypothesis was strong and was supported by current thinking in the field, state that with examples from other projects. Weaknesses might include small sample size, poor task design or additional studies that developed different conclusions. When you write about weaknesses, be sure to include possible reasons and strategies to improve them in future projects.
End your paper with a statement about future research ideas. Propose ideas for building on the author's work. Consider the next logical steps, how they would benefit science and how feasible they are to conduct. For example, a study of teaching language skills to two-year-olds on the Autism Spectrum might be expanded to include two-year-olds with other disorders.