First of all, get enough sleep and eat breakfast the day of the test. Your brain needs the help. Go prepared with extra pens or pencils if you can. Now the writing advice: Before you start writing an answer to an essay question, STOP and think. Make BRIEF notes about what you want to say and add to the list as ideas occur to you. Read each essay question carefully and number each part of the question so that you answer each part. Sometimes an essay question may have two or three parts. If you don't answer them all, you may not get any credit. If the question contains the word NOT, circle it because it reverses the ideas in your brain. If you have only one essay to write, be sure that you revise to make sure that your essay truly answers the question asked, that you have a thesis statement and proof of your ideas, and that you use good mechanics and sentence variety if you can. Sentence variety means using complex sentences instead of only simple and compound which will allow you to use more grown up phrasing. If complex sentences mean nothing to you, be sure that you don't start all your sentences the same way. Good luck and don't panic!
State exams are usually easier than other exams you might have taken in high school : teacher made exams, AP exams, department written finals, etc. So, I wouldn't be too worried about passing them. Just eat well the night before and morning of the exam. Take your time, read things carefully, and do your best.
Get sleep and a good breakfast so you don't feel tired or worn out. To be honest, when I took the HSPE I didn't find it as hard as I thought it was. Just know how to spread out your words in the paragraphs with concrete sentences that back up your claim. Remember to watch out for words like Always and Not! This can really impact what you write about