Read the article carefully as many times as necessary to completely understand what the writer seeks to explain. If you try to critique something you don't entirely follow, you are more likely to present an erroneous point of view. Refer to some other books on the subject if you want greater clarity about some concept.
Read the article again, but now with a critical eye. Observe the facts, examples, measurements and methods the writer has used to prove his point. Note if there are any fallacies or discrepancies in the experimental method the researcher followed. Study the sources the author used and check if they are reliable ones. List your observations regarding the weak points of the article.
Begin your critique with an introductory paragraph. State the title of the article, the author's name, the journal where the article appeared and its publication date. Give a short summary of your impressions about the article.
Present evidence to back up your analysis of the article, giving equal importance to both positive and negative aspects. For example, if the researcher used analytical method X which is inferior to method Y, state this in your critique, along with an explanation of why method Y is considered superior.
Point out any errors you noticed such as the complexity of vocabulary, stilted style of writing, insufficient handling of biases or a flawed logic in the argument. Give examples from the paper to support every point you make, but avoid making your critique sound like a summary of the article.
Conclude your critique by summarizing the major points you make in the body of your thesis. Repeat again the statement you made in the introduction about your opinion about the article, using a different set of words.