It's definitely different for each individual, and I think a lot hinges on who initiated the divorce, what the relationship was like before then, and how the individuals feel about the divorce. For me, I'd put up with a really bad situation for so long that all I felt was relief when it was over...and he moved his girlfriend in two weeks later, so I saw absolutely no point in beating myself up over someone who obviously didn't value me anyway. The day I came back to my hometown and took up temporary residence with my "other mother", my mom came rushing over with chocolates and a cheesecake and was all ready to offer her condolences and help me through this "tough time"...she seemed downright confused about how relaxed and cheerful I was. There were still a lot of hard times ahead as far as custody issues and such, but just getting out of such an unhealthy situation did wonders for me from day one.
Five months later I was officially in another serious relationship, though it had been building for a little while before then. While I still had some baggage from my previous marriage (as did he, though his marriage had been over for 11 years), there wasn't the issue of still being emotionally attached to the ex or anything else that tends to be a major factor in ruining future relationships. The biggest thing was that we'd both previously been with very overbearing and controlling people, so it took a while to get used to the fact that we could just relax, be ourselves, do what we wanted, and even wear the clothes or buy the food we chose ourselves. Now we're married, our baby girl was born three months ago, and all has gone exceptionally well.
Disclaimer: Results not typical ;)