An annulment wipes your marriage off the books, as if it never happened. But understand that there are two types of annulments: civil (by the government) and religious. Obtaining one doesn't mean you've obtained the other. You need to apply for both if you want both.
Know that to obtain a civil annulment, you must prove that there was some kind of mistake when you were married, so that there never was a true marriage.
Find out what the permissible reasons for annulment are in your state. The common reasons are that one person was underage, one person didn't understand he or she was getting married, the marriage could not be consummated, one person was forced to marry or fraud was involved, one person is mentally ill or one person was already married to someone else.
Realize that you probably need to hire an attorney to handle the case for you.
Recognize that an annulment erases your marriage; divides your property and debts, just like a divorce; and determines custody of your children.
Relax with the knowledge that an annulment does not make your children illegitimate. They are and will always be legally legitimate.
Consult your priest for information about an annulment through your church or your rabbi for information about a Get.