Finding mistakes requires concentration and practice. If you are using a computer or word processor, proofread from a printed copy. Proofread it after you have worked on something else. A good method to use is reading or having someone else read your paper aloud, because the ready ear can often hear more mistakes than the weary eye sees. Another method is reading backwards sentence by sentence to put attention on mistakes rather than on the ideas in the paper.
Spelling is an important consideration, also.
Using a spell correction program for computer-generated papers is a good way to start finding spelling mistakes, but words can have correct spelling and still make no sense in a sentence, so more work is required. The word hair is properly spelled but is not the right word for the sentence. A good reference source for the correction of these is The St. Martin's Handbook . In addition to checking for errors, proofread for meaning as well. This example shows that word choice and sequence is very important to the meaning of written material.