The NHL is set up pretty much like most other sports leagues are. For the most part. There are conferences and regional divisions. But there are some quirks in regards to the basics in regards to playoffs berths.
The NHL has been around since 1917. It has a long and storied history that has been written about in a great many books. Hockey players are perhaps the nicest and most humble professional athletes than anyone will ever meet. And its championship trophy, the Stanley Cup, has a much longer history than the league itself - and more of a social life than most celebrities.
But, let's start with the basics. The NHL currently has two conferences and three divisions within each conference. The winner of each division is guaranteed a playoff spot, along with home ice in the first round. The divisions within the Eastern Conference are the Atlantic, the Northeast, and the Southeast. And the divisions within the Western Conference are the Central, the Northwest, and the Pacific.
The Atlanta Thrashers, which were in the Southeast Division, abruptly moved to Winnipeg last summer. They moved so abruptly, in fact, that the NHL decided to leave them in the Southeast Division for the time being. At some point in the next season or two there may be league realignment due to that, and perhaps due to other teams moving as well.
Speaking of Atlanta, there are NHL teams in warm climates, and that seriously upsets hockey traditionalists - they tend to live in Canada, but some are also from the Northeast and the Midwest. Despite the fact that practices and games at all levels are almost always on indoor rinks, these traditionalists seem to think that all of the teams in warm climates need to either be contracted or moved north because hockey should only be played outdoors and/or in areas where it snows. These teams are referred to as "Sun Belt" teams, and that term is usually considered an insult by those saying it.
The so-called Sun Belt teams consist of the Phoenix Coyotes, the Nashville Predators, the Carolina Hurricanes (in Raleigh, NC), the Tampa Bay Lightning, and the Florida Panthers (who play just outside of Fort Lauderdale). Atlanta was also included in the "Sun Belt" group, up until they moved. They do not, however, include the Los Angeles Kings, the Anaheim Ducks, the San Jose Sharks, the Dallas Stars, nor the St. Louis Blues.
Typically, to have that term stuck to a team, they either need to have been relocated or have been an expansion team from the past 20 years, struggling to get fans in the seats (regardless of playoff appearances or not), have ownership issues, and/or aren't doing well in the standings - on top of being located in a warm climate, of course. Dallas was briefly referred to as a Sun Belt team by this crowd when they had their ownership troubles last year, but has since reverted back to non-Sun Belt team status.
The NHL's standings are determined by a win, loss, and overtime loss format. There are two points for a win, no points for a loss, and a point for overtime. The overtime point is not particularly liked by fans, so it's often referred to by many as a charity point, or a "Bettman" point. (Gary Bettman, the league commissioner, is widely disliked by fans.) Overtime consists of a five minute period followed by a three player per team shootout, if necessary.
(A regulation game is 60 minutes, but is broken up into three 20-minute periods with two 20-minute intermissions to resurface the ice; a regulation NHL game typically lasts about two hours and 40 minutes.)
The regular season, which is 82 games, runs from the beginning of October until early April. The post season is considered the NHL's "second season", and runs from mid-April until mid-June. The top eight teams in each conference participate in playoffs, and often the playoff races last until the last week of the season.
The top three seeds in each conference are the division champions, ranked in order of most points in the standings. After that, the rest of the teams are ranked according however many points in the standings teams have, regardless of division. Even if a team in another division in the same conference has a higher point total than the champion of another division, the division champion will be seeded in the top three in the conference.
Every series in playoffs is a best of seven games - Games 1 & 2 at the higher seed, Games 3 & 4 at the lower seed, Game 5 at the higher seed, Game 6 at the lower seed, Game 7 at the higher seed. Being able to start a series at home is considered "home ice". The format for the first round in each conference goes #1 vs. #8, #2 vs. #7, #3 vs. #6, and #4 vs. #5. The second round is the top remaining seed versus the lowest remaining seed, while the middle two seeds are left to play each other, in each conference. Then there are the conference championships followed by the Stanley Cup Final.
The one thing that you need to know about the NHL playoffs is that a player has to be dead in order to not play. After a team falls out, only then do injuries start to trickle out into the media. It's not uncommon to find out that a few players off of each team were playing with broken bones, severely sprained joints, a dislocated something, or some other horrific injury. Even if a guy may have trouble walking, that won't stop him from skating.
And the reason behind this insane practice isn't for the money, or even for the championship. NHL players get a fraction of what they're usually paid during the regular season for playoffs, and no one ever calls themselves "NHL Champions". No, they want the Cup. Unlike in most other sports, it's not a replica, but something that's been associated with hockey in one form or another since 1893. It became the NHL's championship trophy in 1926.
The Stanley Cup is the same trophy that these current NHLers' boyhood idols picked up, that their fathers' boyhood idols picked up, that their grandfathers' boyhood idols picked up, their great-grandfathers' boyhood idols picked up.
In the NHL, you play for a chance to win the Stanley Cup. And if you're lucky enough to make it to the Final and win it, then you're a Stanley Cup Champion, and you get your name added alongside the greatest names that have ever played the game. It's as simple as that.