Study from English grammar textbooks such as "Cambridge Grammar of English" by Ronald Carter and Michael McCarthy. Perfect your understanding of the rules of grammar right from the use of verbs, adverbs, articles and idioms to the construction of sentences. This will help you identify what constitutes a formal tone, which is the very basis of academic English.
Build your vocabulary by reading from literature, academic texts in your subject area and the editorial columns of newspapers. Refer to a dictionary to find the meanings of new words you read. Practice using these words in your academic assignments.
Improve your vocabulary of academic English using the Academic Word List available at the website of the Victoria University of Wellington, New Zealand. This list details 570 word families, which are useful in academic English.
Listen to academic lectures which are available on sites such as Academic Earth. These sites contain lectures on different subjects, and often include transcripts. Read the transcript as you listen to follow what the speaker is saying. Mark the words you find unfamiliar and find their meanings.
Watch news and documentary films on television channels such as CNN, CNBC and BBC. Focus on noticing the difference between the English they use and that which is used in movies and chat shows. Academic English uses an impersonal and objective manner of speech, and avoids the use of slang and jargon. For example, saying "He talked about......" is informal English, whereas "It was argued that...." is more formal.
Get information about the style of academic writing your school requires you to follow. Buy a book that provides these guidelines and study from it to hone your academic writing skills. For example, English classes follow the Modern Language Association style, whereas psychology classes require the American Psychological Association style, and the Chicago Manual of Style is used in workplaces.
Take the quizzes available on websites such as Academic English Café to test your progress with academic English vocabulary and grammar.