In this video Denis Savard explains how to run the Regroup to Backcheck drill. This is a great drill that incorporates a regroup, quick transition, 3 on 2 with a backchecker, and 3 on 3 down low.
To set up the drill place three lines of forwards just inside the blue line and a fourth line (the backcheckers) between two of the lines and slightly behind the start of the other three lines. See the video for a diagram. The two defense will start inline with the dots at center ice. One of the lines of wingers will start with the puck.
The line with the pucks will start on the whistle by passing the puck to the center, the center will pass to the other wing, and that wing will make a pass to the defense. The defense will make a D to D pass and the forwards will work on regrouping with the defense back towards their lines. The forward that has the puck after the regroup will make a pass to the first player in the backchecking line. This player will one touch the puck up to one of the forwards and the forwards will transition back against the defense to make it a 3 on 2 with the backchecker applying pressure from behind.
Teaching players how to backcheck is an important concept. Here are some backcheking systems that can help explain to your players how to backcheck in certain situations.
You can extend this drill so that the players will continue to play 3 on 3 down low if they do not score off of the initial rush. When that happens the backchecker and defrense need to communicate with each other and play man to man defense down low.
Here are some more backchecking drills that work on backchecking on 1 on 1, 2 on 1, and 3 on 2 situations.