I have advice, as a Hawks fan, to impart on your teams for getting a great rebuild done.
1) Suck, really, really bad
Like, so bad that you're guaranteed a top 5 pick perennially. Edmonton, Buffalo, you're on this pretty well, gotta say.
2) Hope the teams ahead of you draft poorly in the first
Do you know who the #1 pick of the 2006 NHL draft was? Erik Johnson, drafted by St. Louis. #2 was Jordan Staal by Pittsburgh. #3 was Jonathan Toews. One of those players has had meteoric success in the pros, the other two, not so much.
3) Invest in your scouts
This is probably the most important, and least obvious key to a successful rebuild.
Obviously, more often than not, the top few players in a given draft will be good or great, with decent careers (Johnson and Staal, at the very least, are still in the NHL 9 years after they were drafted). But you can't stock your roster with nothing but top 5 first round picks, there isn't enough talent to go around for that.
You need to be able to draft well outside the slam dunks. Going back to the Blackhawks, Corey Crawford, Duncan Keith and Brandon Saad were all taken in the second round in their respective drafts. Crawford and Keith were both All-Stars this year, Keith has two Norris trophies and is probably a Hall of Famer, and Saad is a regular first liner above players like Patrick Kane (who's pretty good). Andrew Shaw, Niklas Hjalmarsson and Ben Smith (likely the greatest hockey player born in Winston-Salem North Carolina), were all taken after 100+ other guys. Yeah those three aren't perennial All-Stars or going to have banners or anything, but they form the complimentary players that a great team needs to succeed.
Or you look at the Kings. Players like Tyler Toffoli and Dwight King were both taken outside the first round and have had a legitimate impact on the team. Hell Jonathan Quick, who has been one of the best goaltenders in this decade, was taken in the third round, just a few picks after Kris Letang (a solid member of the Cup winning Pittsburgh core). Both these guys were taken well after guys who don't even have a Wikipedia page.
But it's not just about the draft, scout the programs of other teams too. On December 5, 2005, the Blackhawks traded Matt Ellison (who would play a total of 7 NHL games for the Flyers) and a third round pick (that the Flyers would trade for a couple picks to Montreal) for Eric Meloche (who never played a game for the Blackhawks) and a young winger named Patrick Sharp. Sharp would go on to not only win 2 Stanley Cups, an Olympic Gold Medal, and be an All Star, but would form a very important part of the core that the Blackhawks developed.
Obviously not every trade works out that way, however for what the Blackhawks gave up, even if Sharp hadn't developed into a star, it would not have been a bust.
4) Continue developing your own young players
Continuing with the Blackhawks (they're the team I know best by far, and they have done one of the most successful rebuilds in recent history), not every player was acquired after the team went full rebuild (it's hard to tell, but I would say the nadir was right around the lockout, they certainly hadn't been good for quite some time, but they weren't bad enough to get a rebuild going until then. A position that the Flames and Stars found themselves in for quite some time, they were either just good enough to make the playoffs and not contend, or just bad enough to be the 9 or 10 seed and miss out on the postseason but not get a great pick).
Duncan Keith and Brent Seabrook were both selected pre-lockout, in 2002 and 03 respectively. They were both in the system but not in the big show until after the lockout. The Hawks could have given up on one or both of them and tried to draft for a top D man, or sign one (which they ended up doing with Brian Campbell, but that's a different matter), but they didn't. The braintrust had realized that they both had potential and chose to develop them further into possibly the best defensive pairing (when the Q blender decides to allow it) in the NHL.
What I'm saying is, even if you decide to blow it up and go full rebuild, keep a watchful eye on the young players you already have, some of them might turn out to be just what you need.