There’s more than one way to skin a neutral zone regroup, but one is quite a bit more common and effective than others.
When your team takes over possession of the puck between the blue lines, the players have two options: one is to do what your rec hockey team does, and start skating the other way with it until there’s a problem, and the second is to have a plan.
Ideally, you’d like guys to build up as much speed as possible for the attack, and to have strong support for the puck at all times (the phrase “support the puck” is ubiquitous in hockey dressing rooms).
In order to achieve these goals, you have to start with step one: get the puck back to your defenseman.
Once a defenceman has the puck and sees that there’s no easy, quick-up solution to getting into the offensive zone, he’ll usually move the puck D-to-D to start things in motion.
(Oh man, these diagrams are going to be crude again.)
That defenseman then starts skating the puck up the wall, which forces the opposing team to start applying pressure. There’s no way they’ll allow that d-man to gain the red line (that’s the pressure line – once you let a team over it they can dump it in, so you need to get to them before they get to it), so you’re starting the defenders moving, which is always good.
That d-man will then pass the puck back to his partner (who’s moved into the middle of the ice as last guy back), and will stay on the wall as a return-pass option. The weak side forward will swing LOW (and I mean LOW - coaches freak otherwise), so the three of you are coming up the ice together and the puck is supported on both sides.
The centerman mirrors the initial D-to-D pass as usual (providing a pass option), and finds himself swinging into a crowded lane – a d-man is low in it, and a forward is somewhere around there too. Because you want guys to have their feet moving and the puck to be supported, the center carries on, and the winger on that side comes across hard to A) get moving, and B), support that puck, which will be moving up the other side shortly (or delivered directly to him if the middle lane is clear, which is unlikely).
After the pass is made to the winger on the wall, you have a player with momentum and solid possession of the puck, support so if he’s pressured before the red so he can chip it to his linemate, a centerman with a lot of speed (who can also head over to the strong side if need be, or provide puck support if the middle D-man passes it back to his D-partner), and you’ve spread out your opponent’s neutral zone forcheck.
As I mentioned earlier: this isn’t the only neutral zone regroup teams use, but I think it’s the most common, the most reliable, and the most effective.