This page lists a number of common grammar mistakes. When you click on one of the mistakes mentioned below you'll find a page explaining that mistake in detail, along with suggestions as to how you might avoid repeating that mistake in future essays.
When you get an essay back, look closely to see if there are comments about grammar, comments like comma splice, or sentence fragment. Then come here to see how to correct those mistakes.
You might also find comments suggesting that you need to improve your style. In this case, you should purchase a good style-guide; the university bookstore has a number of good texts you can consult. One of these is Strunk and White'sElements of Style, which is also available online.
Remember not to panic if you find that grammatical errors are plaguing your work. Writing is a craft, not an inborn talent, and anyone can overcome grammatical errors with a bit of perseverance and determination.