Ok, Photoman. You asked the million dollar question. Let me see where to start...
In order to get access to any venue (wether it be a concert, or a sports event, or a movie set), usually you need to contact the organizing party, and secure a Press spot. At places like NHL and NFL, there is probably a ballpark limit of press passes available (Other places like sets or Concerts, you may be given strict regulations, such as length of time you can shoot, or photo styles -non flash, for example- ).
The first and most important question any one of these places will ask you, is " Sure, Mr. xxxxxxx, now who did you say you work with?" ... That would be a great moment to mention your friend the Editor of Sports Illustrated, or the popular Local Daily, and often be able to produce a credential that actually shows you represent them. Once their first concern is satisfied, you will pass onto the Political issue, which is trying to secure a spot for yourself. So remember, Who are you, and Why are you here. (BTW, the statement 'I am a huuuuge fan' does not usually work).
I would start with smaller places, depending where you live, start going to county and state fairs, and gain access to those as a member of the press. Contact their administration, and secure yourself some passes. Do the same at the local racetrack, to gain some extra practice and finesse with PR.
Personally, I have gained entrance to many very interesting places, representing as a member of the press. Although I am but a few minutes away from the 49ers Stadium (I am not sure what the place's name is this week) I am pretty sure I cannot enter the Press area. To give you an example, a few months ago News Photographer Mag (The Natl Press Photog Assoc magazine) did an article on the four guys that shot all 40 superbowls. When I started thinking, these fellers have taken their press spots for 40 years in a row. Not likely that my Daily Planet credential will secure me a space with them or in their place.
I hope this information helps. It never hurts to have a goal to aspire to. NFL is like the ending goal, nothing is better than hanging out with the Big Leaguers. Now map all the points between where you are today and then, and simply take it one step at a time.
Hope this helps.