Think of yourself as a professional reviewer. Hold yourself to high standards, both in terms of your level of understanding of the art and the clarity and strength of your writing. Don't be afraid to seek out subjects for review that are not in the mainstream. In addition to commercial galleries, seek out obscure artists, shows in out-of-the-way places, and work that isn't necessarily popular. If you write about these things with wit and confidence, you will begin to develop your reputation as a dependable reviewer.
Write at a level that is accessible to the widest audience. If you write in an excessively erudite or academic fashion, it will sound like a dissertation. Reviews call for a different style of writing than peer-reviewed research writing. Conversely, don't cater to the lowest common denominator; the writing should have some challenging content in order to keep demanding and educated readers interested.
Begin your essay with the positive aspects of the art you are reviewing. This will tend to present you in a positive light to readers. Don't ignore things that you didn't like, but get to them later in the article. Be respectful but decisive---if there are weaknesses or flaws in the artwork or exhibition, you should clearly cover them. Remain objective in your tone; although it's clear that the review is your opinion, readers are interested in it to the extent that it affects them. Try to put yourself in the readers' place as you are writing and find common ground with them.
Contextualize your subject matter. You will teach your reader more, and make yourself sound more authoritative, if you can discuss not only the artist or artists in the exhibition at hand, but other works and venues that relate to them. By connecting your subject matter with historical examples, precedents, and contemporary issues that are related to it, you will help the reader more fully understand the work.