Aaron is right. The scriptural grounds for divorce are very narrow. So far as I can tell the scriptures do not expressly permit remarriage, but we can assume that if you have the right to a divorce you also have the right to marry. This is God's plan for the family. Unfortunately our culture sees things differently, and it seems Christian marriages fare no better than any others. More than half of all people who marry can expect to be divorced. This presents an enormous problem in the church. If we take a strong position against divorce, barring divorced persons from teaching, holding church offices or being deacons, we lose many of our most valuable members. It's just very difficult to rail against divorce when literally half the people in your congregation have been divorced.
On the other hand, our acceptance of this phenomenon has no doubt contributed to the number of divorces. It wasn't too many years ago that there were real consequences for getting a divorce. Edward VIII abdicated the British throne in 1936 to marry a divorced woman. We have had only one divorced president--Reagan. Being divorced was a barrier to advancement in most careers. People would shun you in social settings. All this made the prospect of divorce a lot more grim and people were very reluctant to take this step on account of the dire consequences. Today these consequences do not exist, so anyone who is unhappy with his or her marriage goes down to the courthouse and gets a divorce. The absence of social consequences encourages divorce.
On the civil side, nearly all states have adopted some form of no-fault divorce. All you have to do to get a divorce is go into court and state under oath that you have lived apart (meaning no sexual activity) for a certain period of time (6 months in my state) and that the marriage is irretrievably broken. It doesn't matter what the other spouse wants. If one spouse says the marriage is irretrievably broken, the court will so find and grant the divorce. The marital property is then divided without regard to any marital misconduct. The law is now such that the contract of marriage is the only contract that can be broken without any negative consequence. The absence of legal consequences encourages divorce.
So what do we do in the church? First of all, we should do more to strengthen marriages. We should redouble our efforts when a couple's marriage is in trouble. However, if one or both parties decide they must be divorced to be happy, we should treat them no different then we would treat someone who is in a homosexual lifestyle. We may lose some members by being hardliners but the church is the body of Christ, not a social club. Of course in either case if the person repents God will forgive them, and if God has forgiven them so should we. So what do we do about persons who remarry? As I stated above, if you have the right to a divorce you also have the right to marry. If you divorced your spouse without scriptural grounds, you can be forgiven but I don't believe God permits remarriage. I believe those who do are living in a state of sin.