The Halo reach DMR is replacing the Br from Halo 3 as the main mid range weapon. The DMR is a hit scan weapon meaning your shot will register instantly much like the Halo 3 sniper. The main difference you will notice immediately is that the DMR is a single shot weapon. The BR was of course a 3 round burst weapon. During the Halo Reach Beta it took 5 near perfect shots to kill an enemy. The BR was known for being a 4 shot weapon in the hands of a skilled player.
The DMR clip is now 15 bullets up from the 12 rounds in the BR. If the weapon damage is not increased in the actual game release this means you can kill 3 enemies per clip if you perfect 5 shot them. Rumors have it that the bloom has been reduced this should make this weapon more manageable than the version that was in the Halo Reach Beta.
In Halo Reach it becomes even more important to shoot as a team and have all four players trying to shoot the same target. This is even more important than in Halo 3 since the DMR at least for now takes 5 instead of 4 shots to kill. So be sure to learn all the call outs so you can team DMR your enemies.
When you make the transition from the BR to the DMR and from Halo 3 to Reach the biggest difference in shooting is the reticule bloom. This means you cannot just spam the trigger and get get shots on your opponent except in some close range battles. Go into some custom games when Reach comes out and practice timing your shots. The key is to watch the bloom. As the bloom gets close to a full reset this is the best time to pull the trigger. Halo Reach will reward those who time their shots and shoot accurately.
As far as leading shots in concerned I cannot say with certainty that you will have to lead your shots in Reach. In Halo 3 shot leading was very important and changed game by game depending on the host. In Halo Reach you will probably still have to lead your shot but not as much since the DMR is a hitscan weapon. The sniper in Halo 3 does not require you lead your shots and so the DMR should function in way similar to this.
For those of you who played Halo 3 and are familiar with the octagon map I suggest you go into forge as soon as reach drops and make or find a similar map. Basically octagon is a map where there is one room with no cover and only a few spawn points. This allows you to keep shooting the entire game and working on your aim. I know as soon as Halo Reach comes out I will be busy making a DMR octagon to get my shot down. I suggest you do the same or get 5 shots in your spartan on the battlefield.