Puck pursuit is all about angles and how you can manipulate those angles to force the puck carrier to go where you want them to go. Simply skating back hard to the absolute middle of your zone is a great skill to teach your novice team, but it gets far more complicated than that at the NHL level.
The idea when pursuing the puck into your teammates is to force the puck carrier to go into where the pressure will occur. Often times you are giving up a soft area on the ice to draw the player and then squeezing that area off.
Sorry, I couldn't find an actual video so I had to screen cap it myself (Shameless plug for Tyler in my browser), just click the link to view the video. Even though this play is a penalty kill, it illustrates the purpose. Ales Hemsky’s only interest is to make sure that the puck heads towards the boards closest to the camera. He ignores the initial puck carrier (Ben Smith I believe) and doesn’t pursue hard until Bickell gets the puck in the middle of the ice. Hemsky takes almost a straight line to get side by side with Bickell, which forces him to go to the boards. The Oilers defence gives enough to let Bickell carry the puck over the blue line, then Hemsky uses the fact that Bickell won’t cross back over the line to hit him along the boards and cause a turnover.
Once Bickell gets the puck, Hemsky skates hard to try and cut the pass off to the outside and to also force Bickell into the area highlighted in Orange. The idea is to box him into the area between the Forward and the defenseman.
Hemsky was able to funnel Bickell into the middle and will now attempt to drive him to the boards. The Oilers defenders back off a bit, giving up the zone, but making sure that they don’t get beat by the other 2 hawks on a chip and chase.
Bickell has basically been contained into the area highlighted on the screen. His only real play with the puck is a chip dump into the corner, with no one going with much speed to get it, which isn’t a bad result for the defensive team in what started out as a 2 on 2 / 3 on 3.
Hemsky finishes the play Driving Bickell into the boards. Bickell still has the chip if he wants it and he’s got an outlet outside the blueline (which loses the zone) , but he’s effectively been eliminated from the play and holding on to the puck allows the Oilers to clear it rather easily.
The idea isn’t to just attack the puck, it’s to recognize where your help is and how you can drive the puck carrier into that help and to use the natural barriers (boards, bluelines) of the rink to your advantage.