If the Church doesn't believe in divorce,
how can some people can get an annulment and get married again?

[Pre-note: If you are considering an annulment yourself, you may be dealing with feelings of shame, disillusionment or embarrassment because of a marriage that has ended in divorce. Try to put aside these feelings and confidently approach your priest or parish staff person who will help you begin a process of healing and new beginnings. Your conversation with your parish representative is a private, pastoral and personal affair. The following is a description of how the process works.]

The procedure through which a union is dissolved by the church's marriage tribunal is called a declaration of nullity. This process is reserved for those marriages that, despite all outward appearances, were never valid from their inception. This process is generally but not always reserved for Catholics who wish to remarry again in the Church after a civil divorce.
Three quick answers to common questions: 1) The Church does not acknowledge the right of civil authorities to dispense from ecclesial vows a couple had professed in church with witnesses. 2) Children born of an annulled marriage are legitimate. 3) Divorce does not prevent a Catholic from receiving communion or participating fully in the life of the Church.

An annulment decree by the Church means that through the process of examination, impediments which existed at the time of marriage rendered it invalid from the beginning. Impediments to marriage include (among others): immaturity, pressure to marry, pre-nuptial agreement, unknown chemical dependency, or a significant psychological or sexual issue.

Annulments are not just for the rich. There is generally a fee (@ $500.00) to process the paper work. In some dioceses, this may be waived or reduced by the local parish. Most people find the annulment process, albeit daunting at the outset, an important-- even therapeutic-- closure to a marriage that was never holy matrimony, (never valid). People find it important to finally have the peace that comes from knowing that they are now unbound and free to marry within the Church if they ever wish to do so.