A divorce by itself (without contested issues of child support, child custody, property division and alimony) is not terribly complicated.  You or your lawyer file a divorce complaint with the clerk of the proper court. The complaint must then be delivered (or "served") to your spouse, either in person or by certified mail.

If you and your spouse can reach a settlement agreement, then the agreement is filed with the Court.  You and your attorney can appear in court after a specified period of time after filing and service of the Complaint and obtain a divorce. 

Once an order is signed by the judge or chancellor, your divorce is final, and you may remarry if you so desire.

You should be aware that the absolute divorce is only one part of the process. It is merely the judicial proclamation that ends your marriage. The complexity of a domestic case arises in deciding other issues such as child custody, child support, division of property, and alimony. These issues are resolved either through negotiation or through a court process.