Write in the third-person ("he" or "she" instead of "I"). Even if you are writing your own biography, writing in the third person is the standard for biography writing, especially on a professional level. Not only does this read better, it prevents the author of the bio from sounding as if he's tooting his own horn. You're writing a brief biography, not an autobiography. This is the key difference. An autobiography is written in first person, a biography is not.
Include information in your brief biography pertinent to the purpose of the biography. A fiction writer's biography should contain a reference to some of her/his better known works. It's acceptable to make reference to upcoming projects as well.
Keep your personal information to a minimum, as well as any phrases that have personal (subjective) overtones, such as ". . . lives in Idaho with his beautiful pet kitten Fluffy." There may be exceptions to this rule if, for instance, you are a comedy writer and your biography has an intentionally funny slant.
Write a longer version of your bio that includes more professional credits, educational background and a brief personal history. This is handy to have for those magazines that ask for longer bios. With a longer version of your brief bio, you have a bit more flexibility in what you can include, though the rule of third-person writing still applies, unless otherwise requested by a publisher.