The first part of the rehearsal dinner night will probably begin at the site of the actual wedding ceremony. This will likely be the first time all the players are in the same place. This is an important time for the Bride and Groom because it gives them a chance to see how the people and the ceremony fit together. Expect them to want to conduct one or two actual walk-throughs of the wedding ceremony. If you're doing a reading, you'll have a chance to walk up to the podium and get a feel for the space and the equipment. The whole rehearsal process can take some time because adjustments are often made as you go. In the end, everyone should have a clear understanding of the order of events and their duties. This includes the Best Man and Groomsmen, so stay sharp!
The rehearsal will be the first time you meet the person officiating the wedding ceremony. It's been my experience that they all run a pretty tight ship. They want this ceremony to go off without any major problems, and they know a big part of that is having everyone pay attention during the rehearsal.
It's often good to remember that the person officiating the event wants to look good when this is all done. No one wants Home Videos. I've been "spoken to" by the person officiating the event more than once for kidding around during the rehearsal.
People start to get a little nervous, tired, and hungry by this time of the day, so patience may be in short supply.
The Best Man should also try to pay attention to other people's jobs at the rehearsal. It's pretty common for people to forget their duties during the confusion of the day of the wedding. For some strange reason people will ask the Best Man and even the Groomsmen for direction, so don't be surprised, and try to be ready with the right answer.
The Standard Order of Events
The order of the ceremony will vary with each wedding, depending on the religion of the Bride and Groom as well as their "feel." The standard wedding begins with the procession, then an introduction by the officiator, a blessing or two, readings and/or songs, the exchange of wedding vows, the exchange of rings, some kisses and clapping, then a few final words of advice or encouragement. It ends with a final procession out and a receiving line, with some birdseed-throwing once the newlyweds arrive. 
More Advice:
- A Sample Best Man Speech
- Tips on Best Man Speeches from the Survey Responses
- The Classic Best Man's Speech
