Pick up a copy of The Elements of Style. Keep it on your desk and grab it whenever you're uncertain about something. Get comfortable with it. Having a reliable guide will help with your review now, and will help more in the future as the rules of proper grammar slowly start to sink in.
Think about your intended audience when you write. Reviews on Eden tend to be casual, comfortable, and conversational. They aren't term papers, and they shouldn't feel like them for the writer or the reader.
Always read back over your work. Don't fall into the trap of thinking that editing is for people who aren't good enough the first time around. It's an invaluable tool.
If you're uncertain about something, read it aloud. It's easier to catch mistakes when you hear them.
Remember why it's important. Writing is about communication, and improper grammar makes it difficult for people to decode what you're trying to say.
You will make mistakes, and there will be things that you don't catch. Don't obsess over it.
If you find yourself making the same mistake continuously, make a mental note of it. It took time and effort for me to anchor the spelling of 'embarrassed' in my mind, or the correct definitions of 'bemused' and 'bespoke'. We all have our weaknesses. Recognizing them is the first step toward conquering them.
For people who feel like they have a solid hold on grammar, offer a helping hand. Remember as well that staying silent about a mistake helps no one.