Recently, The New York Times' "Room for Debate" featured "Why Remarry?", with professors and marriage experts commenting on why people do or don't remarry, the impact of remarriage on children, and the effect of laws and customs on the rate and success of remarriage.
To me, the most interesting contribution came from Stephanie Coontz, author of Marriage, a History: How Love Conquered Marriage, who shared her insights gleaned from interviews with couples who have enjoyed successful second marriages. She found that 1) the partners admitted their mistakes in their first marriages (and resisted the temptation to lay all the blame on their ex-spouses), and 2) the partners had abandoned behavior based on old-fashioned presumptions and stereotypes of gender roles.
There is a clear possibility of interaction between the two—mistakes made in the first marriage may have involved an adherence to strict, traditional gender roles—but nonetheless the first insight is more general and more valuable, especially to younger people leaving one marriage and considering another, but who embraced traditional gender roles less than their parents likely did.
And its lesson is simple: learn from your mistakes. It's natural that, after getting divorced, each ex-partner would like to blame the other for most (if not all) of the things that went wrong in the marriage. Of course, in most cases of failed marriage both ex-partners share the blame, and they can argue endlessly about who did what to whom (and with whom, as the case may be). My point is that assigning blame for what went wrong in the old marriage won't help make the new marriage work better. You may not have been able to fix the first marriage (if you even wanted to), but you can learn from it to help make the second one better.
If, as Plato said, the unexamined life is not worth living, then the unexamined marriage is not worth reliving! After divorcing, you should step back after some time and reflect, whether by yourself or with a good friend or professional. You might want to look at your first marriage like a coach watches game tapes, looking for things his or her team did right and wrong, as well as what the other coach and team did right and wrong. Hopefully, the entire marriage wasn't as rivalrous as competitive sports, but more contentious parts, those you want to learn from, were likely worse! (Not that we want to rule out learning from things that went well in the first marriage, of course.)
Also, remember that, setting aside the issue of children for now, your ex-spouse is not the focus anymore—your new spouse is. It goes without saying that you should never take out your frustrations about your old marriage on your new partner. But while obvious, this is more easily said than done; everyone coming out of a failed relationship has certain buttons that were pushed too often or sensitive spots worn down to the bone, and your new partner will inevitably hit them without knowing to or meaning to. Remember that he or she is starting fresh with you—you can't wipe your memory of those sore spots overnight, but try to keep a generous spirit and give your new partner the benefit of the doubt.
Perhaps the best advice I can give is this: a second marriage is a chance to do it better, to get it right, with someone who deserves your best effort. Learn from the mistakes of the first marriage and then put it behind you so you can focus on the second one—and never have to think about a third!