In short, TPD takes place directly after chapter 181 of the manga. Renji comes to escort a still-wounded Byakuya home, our favorite noble is rather frazzled, and everything goes... uphill from there. The trainwreck basically commences. After initial uncertainties, the two begin a romantic relationship that is of mutual healing and, along the way, quite a few ups and downs.
After a short time together, Renji departs for the living world to help in the war against Aizen. When he returns five years later, the only thing that seems to have changed is Byakuya's relationship with his zanpakutou, which causes a bit of conflict between the two shinigami.
Over time, Renji and Byakuya are married, face more struggles, and eventually start a family. Things settle... eventually. Or did they?
This is just a very, very watered down overview, so go ahead and read the real thing!