NHL 14

Contrary to what Th3 Dude says, there is a bit more to these meters (then again, maybe it varies by difficulty level or what kinds of events are happening around the time, but in my 2 seasons so far this solution seems to be highly over-simplified.)

Essentially, this is your classic happiness balancing act we've seen in several games. In the interview questions and/or life events, you will often be presented with choices that will hurt one group to benefit another. At best some may help 2 or even 3 groups, but generally slower than one that only helps a single group. Here are the secrets to each of the four groups, as I've seen...

Fans - Just keep mentioning them a lot (i.e. "We just go out there and try to make the fans happy") and it doesn't hurt to get a little bit cocky now and then, such as saying you've been on fire recently,etc... though i wouldn't suggest going for the REALLY cocky responses (i.e. "I'm the only good player on this team" etc.) as they hurt your other groups. And if you get a life moment such as a guy approaching you for an autograph, it should go without saying but do what the fans would like.

Teammates - Give them credit... as much as they can stand. If you're asked about your latest hat trick, say how you couldn't have done it without their set up. If you're asked to comment on a teammates success: just always talk them up as much as possible.

Management - Any time you're given the chance to talk about a "gameplan" (in a positive light obviously), DO IT. Also, should be obvious but, if you see an option to talk about how good your management is, do that to. The little less obvious point here is that management LOVES IT when you're nice to your opponents. Any time you're asked about a team you're about to play or just played, talk them up. Management will adore this.

Family - This seems to be the slowest and most difficult to raise early on, but when you get options to talk about your home life (i.e. I keep getting a question asking why I've been playing so well where one of the options is to mention that your pot bellied pig just died) these are the ones to go for. Your family ALSO seems to like the minor cockiness mentioned in the fan description. There also appears to be (though I'm not 100% sure if this is every time or just once in a while) a tie between family rating and income, so accepting endorsements, etc. will probably raise this meter as well.

LIFE DECISIONS - ****MINOR SPOILER AHEAD****
When you're faced with these life decisions, a lot of times they will be even bigger swings in the meters than the interview questions, but will also be a much bigger swing in the meters. I, for example, was given one where teammates had been going out after curfew and the coach was going to call everyone to see who went out and you get the option of going out with them or staying home to answer the call. Obviously, one hurts your management but helps your teammates and the other vice-versa (the remaining two options were varying degrees of siding with the team).... HOWEVER, There can also be other rewards. I chose to stay in and answer the call cause I was working on my management rating... and I was bumped up to a higher line as a "reward", so consider your options carefully.