This can be painful but enlightening. You will find yourself editing as you speak. If you don't know precisely what a word means, either look it up or use another word. If you have to stop and read the sentence, so will your professor. Simplify the sentence to make it clear.
Some people mistake flowery, pretentious, complex, or confusing writing for good writing.
Impress your professor with clear, lucid thoughts, not jargon and showy writing. Look up every word you are not sure about. Obviously, you have to know something is wrong before you can proofread for it. Familiarize yourself with proper usage, punctuation, and grammar. Also, ask someone you trust to read it as well.